{"id":1844,"date":"2021-12-02T21:00:25","date_gmt":"2021-12-02T21:00:25","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=1844"},"modified":"2023-10-03T17:26:45","modified_gmt":"2023-10-03T17:26:45","slug":"clase-digital-6-ecuaciones-fraccionarias-ecuaciones-con-radicales-e-inecuaciones","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-6-ecuaciones-fraccionarias-ecuaciones-con-radicales-e-inecuaciones\/","title":{"rendered":"Clase digital 6. Ecuaciones fraccionarias, ecuaciones con radicales e inecuaciones"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-40 has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-1845\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1.jpg\" style=\"object-position:42% 24%\" data-object-fit=\"cover\" data-object-position=\"42% 24%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1200\" class=\"wp-block-cover__image-background wp-image-1845\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1.jpg\" style=\"object-position:42% 24%\" data-object-fit=\"cover\" data-object-position=\"42% 24%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1-300x225.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1-1024x768.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1-768x576.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/gyrya37faki-1-1536x1152.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\"><br>Ecuaciones fraccionarias, <br>ecuaciones con radicales e inecuaciones<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Bienvenido (a) al sexto tema titulado \u201cEcuaciones fraccionarias y ecuaciones con radicales que originan una ecuaci\u00f3n de segundo grado\u201d. Iniciaremos la clase con los conceptos de fracci\u00f3n y radical. Teniendo los fundamentos claves, mostraremos el procedimiento paso a paso para encontrar sus ra\u00edces.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recuerda que una ecuaci\u00f3n es una igualdad entre expresiones algebraicas en las que intervienen uno o varios valores desconocidos, o inc\u00f3gnitas, y solo es verdadera para ciertos valores de las inc\u00f3gnitas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lo primero que hay que saber es que toda ecuaci\u00f3n algebraica de grado <em><sup>n<\/sup><\/em> con coeficientes reales o complejos tiene al menos una ra\u00edz real o compleja. Este enunciado es el Teorema Fundamental del \u00e1lgebra.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D\u2019Alembert fue el primer matem\u00e1tico que dio una demostraci\u00f3n, pero no era completa.&nbsp;Se considera a Gauss como el primer matem\u00e1tico que brind\u00f3 una demostraci\u00f3n rigurosa.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"1-1-ecuaciones-con-radicales\">1.1. ECUACIONES CON RADICALES<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Una ecuaci\u00f3n con radicales es aquella en la que alguna inc\u00f3gnita aparece en el radicando de un radical. Por ejemplo:&nbsp;&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radicales-1.png\" alt=\"\" class=\"wp-image-2904\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"147\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radicales-1.png\" alt=\"\" class=\"wp-image-2904\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radicales-1.png 349w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radicales-1-300x126.png 300w\" sizes=\"auto, (max-width: 349px) 100vw, 349px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Para resolver ecuaciones con radicales se despeja uno de los radicales aisl\u00e1ndolo en un miembro de la ecuaci\u00f3n (en caso de que sea necesario); a continuaci\u00f3n, se eleva ambos miembros de la ecuaci\u00f3n a una potencia igual al \u00edndice del radical, lo que permitir\u00e1 que desaparezca el radical despejado. Este proceso se repite hasta que se hayan eliminado todos los radicales presentes y entonces se resuelva la ecuaci\u00f3n final que resulta.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Al resolver la ecuaci\u00f3n final, se debe verificar que las ra\u00edces no sean extra\u00f1as con respecto a la ecuaci\u00f3n original, pues como se recordar\u00e1, la elevaci\u00f3n de ambos miembros de una ecuaci\u00f3n a una misma potencia no siempre da como resultado una ecuaci\u00f3n equivalente a la inicial,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Analiza los siguientes ejemplos de ecuaciones con radicales.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primer ejemplo:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-2.png\" alt=\"\" class=\"wp-image-2905\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-2.png\" alt=\"\" class=\"wp-image-2905\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Aplica una de las propiedades de la igualdad para elevar al cuadrado el primer miembro y el segundo miembro de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radicales-3.png\" alt=\"\" class=\"wp-image-2906\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"94\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radicales-3.png\" alt=\"\" class=\"wp-image-2906\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Ahora desarrolla las operaciones: potencia de un radical y la regla del cuadrado de un binomio.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">x + 2 = x<sup>2 <\/sup>-8x + 16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplica la propiedad aditiva de la igualdad para que agrupes los t\u00e9rminos en un solo lado de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">0 = x<sup>2<\/sup> &#8211; 8x + 16 &#8211; x 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes y ordena la ecuaci\u00f3n en forma decreciente:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">0 = x<sup>2<\/sup> &#8211; 9x + 14<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplica la factorizaci\u00f3n de trinomios o la f\u00f3rmula general para resolver la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(x &#8211; 2) (x &#8211; 7) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se obtienen las soluciones: <\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">x &#8211; 2 = 0             <br>x = 2               <br>X &#8211; 7 = 0   <br>x = 7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De las dos soluciones s\u00f3lo x = 7 satisface la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-4.png\" alt=\"\" class=\"wp-image-2907\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"220\" height=\"78\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-4.png\" alt=\"\" class=\"wp-image-2907\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">ya que si sustituyes x = 7  en la ecuaci\u00f3n, se verifica que<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-5.png\" alt=\"\" class=\"wp-image-2908\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"78\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-5.png\" alt=\"\" class=\"wp-image-2908\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">por lo que 9 = 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mientras que x = 2 no satisface la ecuaci\u00f3n <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-6.png\" alt=\"\" class=\"wp-image-2909\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"211\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-6.png\" alt=\"\" class=\"wp-image-2909\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Porque si sustituyes x = 2 en la ecuaci\u00f3n, se obtiene que <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Raducales-7.png\" alt=\"\" class=\"wp-image-2910\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"85\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Raducales-7.png\" alt=\"\" class=\"wp-image-2910\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">como <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-7.png\" alt=\"\" class=\"wp-image-2911\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"156\" height=\"67\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-7.png\" alt=\"\" class=\"wp-image-2911\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">X = 2 no satisface la ecuaci\u00f3n. Por consiguiente, el conjunto soluci\u00f3n es: <strong>{2}<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como segundo ejemplo analiza la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-9.png\" alt=\"\" class=\"wp-image-2912\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"245\" height=\"90\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-9.png\" alt=\"\" class=\"wp-image-2912\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Antes de elevar al cuadrado, es conveniente que apliques la propiedad aditiva de la igualdad para dejar uno de los radicales en un lado de la ecuaci\u00f3n. Este paso reduce el proceso de soluci\u00f3n, tal y como se muestra a continuaci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primero aplica la propiedad aditiva de la igualdad para pasar el radical<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-10.png\" alt=\"\" class=\"wp-image-2913\" style=\"width:52px;height:62px\" width=\"52\" height=\"62\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-10.png\" alt=\"\" class=\"wp-image-2913\" style=\"width:52px;height:62px\" width=\"52\" height=\"62\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">al otro miembro de la igualdad.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-11.png\" alt=\"\" class=\"wp-image-2914\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"222\" height=\"75\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-11.png\" alt=\"\" class=\"wp-image-2914\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Ahora eleva al cuadrado ambos miembros de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-12.png\" alt=\"\" class=\"wp-image-2915\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"84\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-12.png\" alt=\"\" class=\"wp-image-2915\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-12.png 313w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-12-300x81.png 300w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Desarrolla las operaciones (potencia de un radical y cuadrado de un binomio)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-13.png\" alt=\"\" class=\"wp-image-2916\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"77\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-13.png\" alt=\"\" class=\"wp-image-2916\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">De nuevo, aplica la propiedad aditiva de la igualdad para que dejes el t\u00e9rmino con radical<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-14.png\" alt=\"\" class=\"wp-image-2917\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"127\" height=\"85\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-14.png\" alt=\"\" class=\"wp-image-2917\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">en un miembro de la ecuaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-15.png\" alt=\"\" class=\"wp-image-2918\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"84\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-15.png\" alt=\"\" class=\"wp-image-2918\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-16.png\" alt=\"\" class=\"wp-image-2919\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"153\" height=\"75\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-16.png\" alt=\"\" class=\"wp-image-2919\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-16.png 153w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-16-150x75.png 150w\" sizes=\"auto, (max-width: 153px) 100vw, 153px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Vuelve a elevar al cuadrado ambos miembros de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-17.png\" alt=\"\" class=\"wp-image-2920\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"209\" height=\"73\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-17.png\" alt=\"\" class=\"wp-image-2920\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Desarrolla las operaciones (cuadrado de un monomio)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>1 = 4. x<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplica la propiedad aditiva de la igualdad para despejar la variable<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-18.png\" alt=\"\" class=\"wp-image-2922\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"103\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-18.png\" alt=\"\" class=\"wp-image-2922\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Si sustituyes en la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-19.png\" alt=\"\" class=\"wp-image-2924\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-19.png\" alt=\"\" class=\"wp-image-2924\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"109\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-19.png\" alt=\"\" class=\"wp-image-2924\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">en la ecuaci\u00f3n<strong> <\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-20.png\" alt=\"\" class=\"wp-image-2925\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"247\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-20.png\" alt=\"\" class=\"wp-image-2925\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"> obtienes que:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-21.png\" alt=\"\" class=\"wp-image-2926\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"221\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-21.png\" alt=\"\" class=\"wp-image-2926\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-22.png\" alt=\"\" class=\"wp-image-2927\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"189\" height=\"110\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-22.png\" alt=\"\" class=\"wp-image-2927\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-23.png\" alt=\"\" class=\"wp-image-2928\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"141\" height=\"115\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-23.png\" alt=\"\" class=\"wp-image-2928\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Por lo que <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-19.png\" alt=\"\" class=\"wp-image-2924\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-19.png\" alt=\"\" class=\"wp-image-2924\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"109\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-19.png\" alt=\"\" class=\"wp-image-2924\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">no es soluci\u00f3n y por lo tanto soluci\u00f3n es <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-24.png\" alt=\"\" class=\"wp-image-2929\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"44\" height=\"71\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-24.png\" alt=\"\" class=\"wp-image-2929\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como tercer ejemplo analiza la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-25.png\" alt=\"\" class=\"wp-image-2930\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"58\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-25.png\" alt=\"\" class=\"wp-image-2930\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-25.png 349w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-Radical-25-300x50.png 300w\" sizes=\"auto, (max-width: 349px) 100vw, 349px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Aplica una de las propiedades de la igualdad para elevar al cuadrado el primer miembro y el segundo miembro de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-26.png\" alt=\"\" class=\"wp-image-2931\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"100\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-26.png\" alt=\"\" class=\"wp-image-2931\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-26.png 467w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-26-300x64.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Desarrolla las operaciones (cuadrado de un binomio y de un radical)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-27.png\" alt=\"\" class=\"wp-image-2932\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"560\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-27.png\" alt=\"\" class=\"wp-image-2932\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-27.png 560w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-27-300x43.png 300w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Aplica la propiedad aditiva para despejar el t\u00e9rmino<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-28.png\" alt=\"\" class=\"wp-image-2933\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"212\" height=\"68\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-28.png\" alt=\"\" class=\"wp-image-2933\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">que tiene radical<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-29.png\" alt=\"\" class=\"wp-image-2934\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"517\" height=\"75\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-29.png\" alt=\"\" class=\"wp-image-2934\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-29.png 517w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-29-300x44.png 300w\" sizes=\"auto, (max-width: 517px) 100vw, 517px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-31.png\" alt=\"\" class=\"wp-image-2937\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"247\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-31.png\" alt=\"\" class=\"wp-image-2937\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-31.png 353w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-31-300x210.png 300w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Eleva al cuadrado ambos miembros de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-32.png\" alt=\"\" class=\"wp-image-2938\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"414\" height=\"170\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-32.png\" alt=\"\" class=\"wp-image-2938\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-32.png 414w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radicales-32-300x123.png 300w\" sizes=\"auto, (max-width: 414px) 100vw, 414px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Agrupa los t\u00e9rminos en un solo lado de la ecuaci\u00f3n<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x<sup>2<\/sup> &#8211; x &#8211; 12 -x<sup>2<\/sup> -2x &#8211; 1 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suma los t\u00e9rminos semejantes y ordena la ecuaci\u00f3n<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>&#8211; 3x &#8211; 13 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Despeja la variable<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-33.png\" alt=\"\" class=\"wp-image-2939\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"299\" height=\"83\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-33.png\" alt=\"\" class=\"wp-image-2939\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Comprueba si<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-34.png\" alt=\"\" class=\"wp-image-2940\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"134\" height=\"96\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/E-radical-34.png\" alt=\"\" class=\"wp-image-2940\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">es soluci\u00f3n de la ecuaci\u00f3n. Te invito a analizar los siguientes videos en donde se explica a detalle el procedimiento para resolver ecuaciones con radicales.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><a href=\"https:\/\/es.khanacademy.org\/math\/algebra-home\/alg-radical-eq-func\/alg-solving-square-root-equations\/v\/solving-radical-equations\">Resolver ecuaciones con ra\u00edces cuadradas: una soluci\u00f3n<\/a><\/strong><\/li>\n\n\n\n<li><a href=\"https:\/\/es.khanacademy.org\/math\/algebra-home\/alg-radical-eq-func\/alg-solving-square-root-equations\/v\/solving-square-root-equations-w-two-solutions?modal=1\"><strong>Resolver ecuaciones con ra\u00edces cuadradas: dos soluciones<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/es.khanacademy.org\/math\/algebra-home\/alg-radical-eq-func\/alg-solving-square-root-equations\/v\/solving-square-root-equations-w-no-solution\"><strong>Resolver ecuaciones con ra\u00edces cuadradas: sin soluci\u00f3n<\/strong><\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"1-2-solucion-de-ecuaciones-fraccionarias-de-segundo-grado\">1.2 SOLUCI\u00d3N DE ECUACIONES FRACCIONARIAS DE SEGUNDO GRADO.<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">La ecuaci\u00f3n fraccionaria de segundo grado la puedes resolver mediante el siguiente procedimiento:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Primero determina el denominador com\u00fan.<\/li>\n\n\n\n<li>Luego, por medio de la propiedad multiplicativa, multiplica cada t\u00e9rmino de la ecuaci\u00f3n por el denominador com\u00fan.<\/li>\n\n\n\n<li>Despu\u00e9s, desarrolla las operaciones que resultan.<\/li>\n\n\n\n<li>Por \u00faltimo, mediante la propiedad aditiva, agrupa los t\u00e9rminos en un solo lado de la ecuaci\u00f3n y aplica la f\u00f3rmula general o la factorizaci\u00f3n.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Como ilustraci\u00f3n de este procedimiento, asimila la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/Ecuacion-1.png\" alt=\"\" class=\"wp-image-2941\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"84\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/Ecuacion-1.png\" alt=\"\" class=\"wp-image-2941\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Primero determina el denominador com\u00fan. El denominador com\u00fan de <em>x y 4<\/em> es 4x; y la soluci\u00f3n no puede ser x = 0, porque no existe la divisi\u00f3n entre cero.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego, por medio de la propiedad multiplicativa, multiplica por 4x cada t\u00e9rmino de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/2.png\" alt=\"\" class=\"wp-image-2942\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"332\" height=\"93\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/2.png\" alt=\"\" class=\"wp-image-2942\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/2.png 332w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/2-300x84.png 300w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Mediante esta operaci\u00f3n elimina los denominadores 4(2 &#8211; x) &#8211; x (x) = 4x. Ahora desarrolla las operaciones:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>8 &#8211; 4x &#8211; x<sup>2<\/sup> = 4x<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, mediante la propiedad aditiva, agrupa los t\u00e9rminos en el primer miembro (lado izquierdo) de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>8 &#8211; 4x &#8211; x<sup>2<\/sup> &#8211; 4x = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes y ordena los t\u00e9rminos de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>-x<sup>2 <\/sup>&#8211; 8x + 8 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si utilizas la f\u00f3rmula general<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/4.png\" alt=\"\" class=\"wp-image-2943\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"100\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/4.png\" alt=\"\" class=\"wp-image-2943\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/4.png 274w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/4-272x100.png 272w\" sizes=\"auto, (max-width: 274px) 100vw, 274px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Es necesario que identifiques que: <em>a<\/em> = -1,   <em> b<\/em>= -8.   <em> c<\/em> = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mediante la propiedad de sustituci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/5.png\" alt=\"\" class=\"wp-image-2944\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"715\" height=\"102\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/5.png\" alt=\"\" class=\"wp-image-2944\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/5.png 715w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/5-300x43.png 300w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Concluye que la soluci\u00f3n es<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/6.png\" alt=\"\" class=\"wp-image-2945\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"112\" height=\"70\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/6.png\" alt=\"\" class=\"wp-image-2945\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como segundo ejemplo, analiza la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/7.png\" alt=\"\" class=\"wp-image-2946\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"175\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/7.png\" alt=\"\" class=\"wp-image-2946\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Primero determina el denominador com\u00fan x( 1 + x), y la soluci\u00f3n no puede ser x = 0<strong> ni<\/strong> x = &#8211; 1, porque no existe la divisi\u00f3n entre cero. Luego, por medio de la propiedad multiplicativa, multiplica por x (1 + x) la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/8.png\" alt=\"\" class=\"wp-image-2947\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"114\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/8.png\" alt=\"\" class=\"wp-image-2947\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/8.png 512w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/8-300x67.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Mediante esta operaci\u00f3n elimina los denominadores:<strong> (1+x)(1 &#8211; x) = x(4) -2.x (1 +x)<\/strong>. Ahora desarrolla de las operaciones: <strong>1 &#8211; x<sup>2<\/sup> = 4x &#8211; 2x &#8211; 2x<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, mediante la propiedad aditiva, agrupa los t\u00e9rminos en el primer miembro (lado izquierdo) de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong> 1 &#8211; x<sup>2<\/sup> = -4x + 2x + 2x<sup>2<\/sup> = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes y ordena la ecuaci\u00f3n: <strong>x<sup>2<\/sup> + 2x + 1 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Y concluye que soluci\u00f3n es: <strong>x = 1<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como tercer ejemplo, analiza la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/9.png\" alt=\"\" class=\"wp-image-2948\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"237\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/9.png\" alt=\"\" class=\"wp-image-2948\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Primero determina el denominador com\u00fan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El denominador com\u00fan es (x + 2)(x &#8211; 1) (x + 3), y la soluci\u00f3n no puede ser x = -2.    x = 1, y x = -3, porque no existe la divisi\u00f3n entre cero. Luego, por medio de la propiedad multiplicativa, multiplica por (x + 2)(x &#8211; 1)(x + 3) la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/10.png\" alt=\"\" class=\"wp-image-2949\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"813\" height=\"128\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/10.png\" alt=\"\" class=\"wp-image-2949\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/10.png 813w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/10-300x47.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/10-768x121.png 768w\" sizes=\"auto, (max-width: 813px) 100vw, 813px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Mediante esta operaci\u00f3n elimina los denominadores:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>(x &#8211; 1)(x + 3)(2) = (x + 2) (x + 3)(1) &#8211; (x + 2)(x -1) (1)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora desarrolla las operaciones:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>(x<sup>2<\/sup> + 2x &#8211; 3)(2) = (x<sup>2 <\/sup>+ 5x + 6)(1) &#8211; (x<sup>2<\/sup> + x &#8211; 2)(1)<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>2x<sup>2<\/sup> +4x &#8211; 6 = x<sup>2<\/sup> + 5x + 6 &#8211; x<sup>2<\/sup> &#8211; x +2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, mediante la propiedad aditiva, agrupa los t\u00e9rminos en el primer miembro (lado izquierdo) de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>2x<sup>2<\/sup> + 4x &#8211; 6 &#8211; x<sup>2<\/sup> -5x &#8211; 6 + x<sup>2 <\/sup>+x -2 =0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes y ordena los t\u00e9rminos:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>2x<sup>2<\/sup> &#8211; 14 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como es una ecuaci\u00f3n cuadr\u00e1tica pura de la forma <strong><em>ax<sup>2<\/sup> + c = 0<\/em><\/strong>, despeja la variable:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/11.png\" alt=\"\" class=\"wp-image-2950\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"144\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/11.png\" alt=\"\" class=\"wp-image-2950\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Y concluye que la soluci\u00f3n<strong> <\/strong>es <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/12.png\" alt=\"\" class=\"wp-image-2951\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"116\" height=\"49\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/12.png\" alt=\"\" class=\"wp-image-2951\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como cuarto ejemplo, analiza la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/13.png\" alt=\"\" class=\"wp-image-2952\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"536\" height=\"114\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/13.png\" alt=\"\" class=\"wp-image-2952\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/13.png 536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/13-300x64.png 300w\" sizes=\"auto, (max-width: 536px) 100vw, 536px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Primero determina el denominador com\u00fan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El denominador com\u00fan es (x + 2)(x + 1)(x -4),  y la soluci\u00f3n no puede ser x = -2,   x = 4,  y x= 1, porque no existe la divisi\u00f3n entre cero. Luego, por medio de la propiedad multiplicativa, multiplica por (x + 2)(x +1) (x &#8211; 4) la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/14.png\" alt=\"\" class=\"wp-image-2953\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"789\" height=\"73\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/14.png\" alt=\"\" class=\"wp-image-2953\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/14.png 789w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/14-300x28.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/14-768x71.png 768w\" sizes=\"auto, (max-width: 789px) 100vw, 789px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Mediante esta operaci\u00f3n elimina los denominadores:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>(x &#8211; 4)(x) = (x + 2)(2) &#8211; (x + 1) (1)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora desarrolla las operaciones:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x<sup>2<\/sup> -4x = 2x + 4 &#8211; x &#8211; 1<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, mediante la propiedad aditiva, agrupa los t\u00e9rminos en el primer miembro (lado izquierdo) de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x<sup>2<\/sup> &#8211; 4x + 2x + 4 + x + 1 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes y ordena los t\u00e9rminos de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x<sup>2 <\/sup>&#8211; 5x &#8211; 3 = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si utilizas la f\u00f3rmula general<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/15.png\" alt=\"\" class=\"wp-image-2954\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"251\" height=\"113\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/15.png\" alt=\"\" class=\"wp-image-2954\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Primero identifica que: <em>a <\/em>= 1,   <em>b<\/em> = -5,   <em>c<\/em> = -3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego aplica la propiedad de sustituci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/16.png\" alt=\"\" class=\"wp-image-2955\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"745\" height=\"123\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/16.png\" alt=\"\" class=\"wp-image-2955\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/16.png 745w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/16-300x50.png 300w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Y concluye que la soluci\u00f3n es<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/17.png\" alt=\"\" class=\"wp-image-2956\" style=\"width:170px;height:89px\" width=\"170\" height=\"89\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/17.png\" alt=\"\" class=\"wp-image-2956\" style=\"width:170px;height:89px\" width=\"170\" height=\"89\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como \u00faltimo ejemplo analiza la soluci\u00f3n de la ecuaci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/18.png\" alt=\"\" class=\"wp-image-2957\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"405\" height=\"78\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/18.png\" alt=\"\" class=\"wp-image-2957\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/18.png 405w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/18-300x58.png 300w\" sizes=\"auto, (max-width: 405px) 100vw, 405px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Primero factorizar los denominadores para que determines el denominador com\u00fan:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/19.png\" alt=\"\" class=\"wp-image-2958\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"555\" height=\"126\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/19.png\" alt=\"\" class=\"wp-image-2958\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/19.png 555w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/19-300x68.png 300w\" sizes=\"auto, (max-width: 555px) 100vw, 555px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Despu\u00e9s determina el denominador com\u00fan (x + 2)(x &#8211; 2)(x &#8211; 3), y la soluci\u00f3n no puede ser x = 12,    x = 2,  y   x = 3, porque no existe la divisi\u00f3n entre cero.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplica la propiedad multiplicativa y multiplica por (x + 2)(x &#8211; 2)(x -3) la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/20.png\" alt=\"\" class=\"wp-image-2959\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"767\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/20.png\" alt=\"\" class=\"wp-image-2959\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/20.png 767w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/20-300x37.png 300w\" sizes=\"auto, (max-width: 767px) 100vw, 767px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Por medio de esta operaci\u00f3n elimina los denominadores: (x &#8211; 3)(x) = (x + 2)(2) &#8211; (x &#8211; 2)(1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Desarrolla las operaciones: x<sup>2<\/sup> &#8211; 3x &#8211; 2x &#8211; 4 + x &#8211; 2 = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduce los t\u00e9rminos semejantes y ordena la ecuaci\u00f3n: X<sup>2<\/sup> &#8211; 4x &#8211; 6 = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si utilizas la f\u00f3rmula general<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/21.png\" alt=\"\" class=\"wp-image-2960\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"110\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/21.png\" alt=\"\" class=\"wp-image-2960\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Identifica que: a = 1,   b= -4,   c = -6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplica la propiedad de sustituci\u00f3n<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/22.png\" alt=\"\" class=\"wp-image-2961\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"719\" height=\"113\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/22.png\" alt=\"\" class=\"wp-image-2961\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/22.png 719w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/22-300x47.png 300w\" sizes=\"auto, (max-width: 719px) 100vw, 719px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Y concluir que la soluci\u00f3n es<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/23.png\" alt=\"\" class=\"wp-image-2962\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"92\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/12\/23.png\" alt=\"\" class=\"wp-image-2962\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Una serie de problemas del mundo real pueden ser modelados con ecuaciones radicales. Cuando nos encontramos con un problema donde una variable aparece dentro de un radical, elevamos ambos lados a la misma potencia para eliminar el radical, y luego resolvemos la variable.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En el estudio de la geometr\u00eda anal\u00edtica, espec\u00edficamente en el tema \u201cdistancia entre dos puntos\u201d se presentan ecuaciones con ra\u00edces cuadradas, su soluci\u00f3n consiste en transformar la ecuaci\u00f3n original en una ecuaci\u00f3n equivalente sin radicales. Para lograr esto, es necesario que apliques las propiedades de la igualdad para elevar al cuadrado ambos miembros de la ecuaci\u00f3n, as\u00ed como el cuadrado de un binomio y el procedimiento de soluci\u00f3n de ecuaciones.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aguilar, A. (2009). Matem\u00e1ticas Simplificadas. (2a ed.). M\u00e9xico: Pearson. Cap. 12, pp. 497 a 511<\/li>\n\n\n\n<li>Araya, J. A., Murillo, M., &amp; Soto, A. (2000). Matem\u00e1tica b\u00e1sica con aplicaciones. Costa Rica: EUNED. Cap. 2, pp. 62-65<\/li>\n\n\n\n<li>Baldor, A. (2017). \u00c1lgebra. (3a ed.). M\u00e9xico: Grupo Editorial Patria. Cap. XXXIII, pp. 446-459<\/li>\n\n\n\n<li>Alberro, A., Benjumeda, F., &amp; Garc\u00eda, R. (2013). Matem\u00e1ticas 1. M\u00e9xico: SM. Cap. 9, pp. 207-230<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n Bienvenido (a) al sexto tema titulado \u201cEcuaciones fraccionarias y ecuaciones con radicales que originan una ecuaci\u00f3n de segundo grado\u201d. Iniciaremos la clase con los conceptos de fracci\u00f3n y radical. Teniendo los fundamentos claves, mostraremos el procedimiento paso a paso para encontrar sus ra\u00edces. Recuerda que una ecuaci\u00f3n es una igualdad entre expresiones algebraicas en &#8230; <a title=\"Clase digital 6. Ecuaciones fraccionarias, ecuaciones con radicales e inecuaciones\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-6-ecuaciones-fraccionarias-ecuaciones-con-radicales-e-inecuaciones\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 6. Ecuaciones fraccionarias, ecuaciones con radicales e inecuaciones\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[83,84],"tags":[41,85,86],"class_list":["post-1844","post","type-post","status-publish","format-standard","hentry","category-bachillerato-general","category-algebra-ii","tag-clase-digital","tag-neba04002","tag-sandra-patricia-arriaga-martinez"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1844","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=1844"}],"version-history":[{"count":6,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1844\/revisions"}],"predecessor-version":[{"id":29838,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1844\/revisions\/29838"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=1844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=1844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=1844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}