Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 361]
Code Context
                $n = array_keys($lista,$lecture["Lecture"]["id"]);

                if($n[0]-1 == 0){
$playlist	=	array(
	"Playlist" => array(
	"id" => "4",
	"name" => "Álgebra",
	"slug" => "algebra",
	"number" => "2",
	"description" => "Rama que estudia las reglas de las expresiones y ecuaciones con variables.",
	"lateral" => "1",
	"image" => "wE6OydOzC-k",
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)
$video	=	array(
	"Video" => array(
	"id" => "115",
	"name" => "Determinantes (sistemas lineales 3x3)",
	"youtube" => "sS-vy-es0j0",
	"slug" => "determinantes-sistemas-lineales-3x3",
	"date" => "2014-10-06 02:08:12",
	"mp4" => "https://dl-web.dropbox.com/get/Videos_math2me_mp4_480p/%C3%81lgebra_m2m_480p/Cap%C3%ADtulo%20IX.%20Ecuaciones%20simult%C3%A1neas%20lineales%203x3/Determinantes%20(sistemas%20lineales%203x3).mp4?_subject_uid=70082452&w=AADs7k-YnAc7pwrPEELB3a488H6qRLm5HfLLj0QtJZqPVg&dl=1",
	"flv" => "",
	"exercise" => "",
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),
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$vID	=	"115"
$params_p	=	array(
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),
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)
)
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$lecture	=	false
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$positions	=	array(
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),
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)
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),
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)
$id	=	"4"
$title	=	"Determinantes (sistemas lineales 3x3) @ math2me.com"
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$n	=	array()
PlaylistController::video() - APP/Controller/PlaylistController.php, line 361
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 364]
Code Context
                    $anterior = null;
                }else{
                    $anterior =$lista[$n[0]-1];
$playlist	=	array(
	"Playlist" => array(
	"id" => "4",
	"name" => "Álgebra",
	"slug" => "algebra",
	"number" => "2",
	"description" => "Rama que estudia las reglas de las expresiones y ecuaciones con variables.",
	"lateral" => "1",
	"image" => "wE6OydOzC-k",
	"index" => "0"
),
	"Lecture" => array(
	array(),
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$n	=	array()
PlaylistController::video() - APP/Controller/PlaylistController.php, line 364
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  -1 [APP/Controller/PlaylistController.php, line 364]
Code Context
                    $anterior = null;
                }else{
                    $anterior =$lista[$n[0]-1];
$playlist	=	array(
	"Playlist" => array(
	"id" => "4",
	"name" => "Álgebra",
	"slug" => "algebra",
	"number" => "2",
	"description" => "Rama que estudia las reglas de las expresiones y ecuaciones con variables.",
	"lateral" => "1",
	"image" => "wE6OydOzC-k",
	"index" => "0"
),
	"Lecture" => array(
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	array(),
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$n	=	array()
PlaylistController::video() - APP/Controller/PlaylistController.php, line 364
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 366]
Code Context
                    $anterior =$lista[$n[0]-1];
                }
                if($n[0]+1 > count($lista)){
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$anterior	=	null
PlaylistController::video() - APP/Controller/PlaylistController.php, line 366
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 369]
Code Context
                    $siguiente = null;
                }else{
                    $siguiente = $lista[$n[0]+1];
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PlaylistController::video() - APP/Controller/PlaylistController.php, line 369
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

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Notice (8): Undefined offset:  0 [APP/View/Playlist/video-menu.ctp, line 382]
Code Context
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              <a class="btn dropdown-toggle video-name" data-toggle="dropdown" href="#">

               <?= $video["Video"]["name"]?>  [<?= $pos[0] ?>/<?= $total ?>]
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[main] - APP/webroot/index.php, line 96

/317]

---

Álgebra

I. Traducción de expresiones algebraicas

• 1. Traducción de lenguaje común a algebraico
• 2. Traducir lenguaje común a algebraico│ejercicio 1
• 3. Traducir lenguaje común a algebraico│ejercicio 2
• 4. Traducir un enunciado a expresión matemática
• 5. Traducción de lenguaje algebraico a común
• 6. Traducir lenguaje algebraico a común│compilado
• 7. Ejercicio de traducir una ecuación a un lenguaje verbal
• 8. Traducción + Interpretación = Ecuación
• 9. Sustituir valores en una expresión algebraica│ejercicio 1
• 10. Sustituir valores en una expresión algebraica│ejercicio 2
• 11. Sustituir valores en una expresión algebraica│ejercicio 3
• 12. Sustituir valores en una expresión algebraica│ejercicio 4

II. Razones y proporciones

• 13. Concepto de razón
• 14. Razones│ejercicio 1
• 15. Razones│ejercicio 2
• 16. Concepto de proporción
• 17. Propiedades de las proporciones
• 18. Proporciones│ ejercicio 1
• 19. Proporciones│ejercicio 2
• 20. Proporciones│ejercicios
• 21. Regla de tres simple
• 22. Regla de tres simple│ejercicio 1
• 23. Regla de tres simple│ejercicio 2
• 24. Regla de tres simple│ejercicio 3
• 25. Regla de tres simple│ejercicio 4
• 26. Regla de tres simple│ejercicio 5
• 27. Regla de tres simple│ejercicio 6
• 28. Intro a la regla de tres simple│directa e inversa
• 29. Regla de tres simple │variación inversa 1
• 30. Regla de tres simple│directas e inversas
• 31. Regla de tres simple│variación directa
• 32. Regla de tres simple│variación inversa 1
• 33. Regla de tres simple│variación inversa 2
• 34. Regla de tres simple│mixtas
• 35. Porcentajes
• 36. Porcentajes│ejercicio 1
• 37. Porcentajes│ejercicio 2
• 38. Porcentajes│ejercicio 3

III. Polinomios

• 39. Conceptos importantes de los polinomios
• 40. Identificar el concepto de polinomio
• 41. Identificar el uso de un exponente en un monomio
• 42. Reducir términos semejantes│ejercicio 1
• 43. Reducir términos semejantes│ejercicio 2
• 44. Reducir términos semejantes - ejercicio 3
• 45. Reducir términos semejantes│ejercicio 4
• 46. Reducir términos semejantes│ejercicio 5
• 47. Reducir términos semejantes│ejercicio 6
• 48. Reducir términos semejantes│ejercicio 7
• 49. Reducir términos semejantes│ejercicio 8
• 50. Reducir términos semejantes│compilado
• 51. Reducir términos semejantes con fracciones│ej. 1
• 52. Reducir términos semejantes│problema 1
• 53. Suma y resta de polinomios
• 54. Suma de expresiones algebraicas
• 55. Suma de expresiones algebraicas │ fracciones
• 56. Signos de agrupación en polinomios
• 57. Reducir términos con parentésis│ejercicio 1
• 58. Reducir términos con parentésis│ejercicio 2
• 59. Reducir términos con parentésis│ejercicio 3
• 60. Reducir términos con parentésis│ejercicio 4
• 61. Reducir términos con parentésis│ejercicio 5
• 62. Reducir términos con parentésis│ejercicio 6
• 63. Reducir términos con parentésis│ejercicio 7
• 64. Leyes de los exponentes
• 65. Leyes de los exponentes│ejercicio 1
• 66. Leyes de los exponentes│ejercicio 2
• 67. Leyes de los exponentes│ejercicio 3
• 68. Leyes de los exponentes│ejercicio 5
• 69. Leyes de los exponentes│ejercicio 4
• 70. Leyes de los exponentes│ejercicio 6
• 71. Leyes de los exponentes│ejercicio 7
• 72. Leyes de los exponentes│ejercicio 8
• 73. Leyes de los exponentes│ejercicio 9
• 74. Leyes de los exponentes│ejercicio 10
• 75. Leyes de los exponentes│ejercicio 11
• 76. Leyes de los exponentes│compilado
• 77. Multiplicación de polinomios
• 78. Multiplicación de polinomios│ejercicio 1
• 79. Multiplicación de polinomios│ejercicio 2
• 80. Multiplicación de polinomios│ejercicio 3
• 81. Multiplicación de polinomios│ejercicio 4
• 82. Multiplicación de polinomios│ejercicio 5
• 83. Multiplicación de polinomios│ejercicio 6
• 84. Multiplicación de polinomios│ejercicio 7
• 85. Multiplicación de polinomios│ejercicio 8
• 86. Multiplicación de polinomios│problema 1
• 87. Multiplicación de polinomios│problema 2
• 88. División de polinomios
• 89. División de polinomios│ejercicio 1
• 90. División de polinomios│ejercicio 2
• 91. División de polinomios│ejercicio 3
• 92. División de polinomios│ejercicio 4
• 93. División de operaciones con paréntesis│ejercicio 1
• 94. Fracciones combinadas con X │ejercicio 1

IV. Productos notables

• 95. Binomio con término común
• 96. Binomios conjugados - productos notables
• 97. Binomios conjugados│ejercicio 1
• 98. Binomios conjugados│raíz cuadrada│ej 1
• 99. Binomios conjugados│raíz cuadrada│ej 2
• 100. Binomios conjugados│raíz cuadrada│ej 3
• 101. Binomios conjugados│raíz cuadrada│ej 4
• 102. Binomio al cuadrado
• 103. Binomio al cuadrado│ejercicio 1
• 104. Binomio al cuadrado│ejercicio 2
• 105. Binomio al cuadrado│ejercicio 3
• 106. Binomio al cuadrado│ejercicio 4
• 107. Binomio con exponente negativo
• 108. Binomio al cuadrado con fracciones
• 109. Binomio al cuadrado con fracciones│ejercicio 1
• 110. Identificar a un binomio al cuadrado
• 111. Ejercicio para desarrollar un binomio al cuadrado
• 112. Binomio al cubo
• 113. Binomio al cubo │ejercicio 1
• 114. Binomio a la cuarta
• 115. Binomio a la cuarta│ejercicio 1
• 116. Productos notables - completo
• 117. Productos notables │ binomios con término común
• 118. Productos notables│ejercicio 1
• 119. Productos notables│problema 1
• 120. Triángulo de Pascal y binomio de Newton

V. Factorización

• 121. Métodos de factorización
• 122. Factorización por factor común
• 123. Factorización por factor común con fracciones
• 124. Factorización por factor común│ejercicio 1
• 125. Factorización por factor común│ejercicio 2
• 126. Factorización por factor común│ejercicio 3
• 127. Diferencia de cuadrados │ factorización
• 128. Factorización por diferencia de cuadrados│ej 1
• 129. Factorización por diferencia de cuadrados│ej 2
• 130. Factorización por diferencia de cuadrados│ej 3
• 131. Diferencia de cuadrados│problema 1
• 132. Factorización de un trinomio x²+bx+c
• 133. Factorización de un trinomio │ x²+bx+c
• 134. Factorización de un trinomio x²+bx+c│ejercicio 1
• 135. Factorización de un trinomio x²+bx+c│ejercicio 2
• 136. Factorización de un trinomio x²+bx+c│problema 1
• 137. Factorización de un trinomio ax²+bx+c
• 138. Factorización de un trinomio │ ax²+bx+c
• 139. Factorización de un trinomio ax²+bx+c│ejercicio 1
• 140. Factorización de un trinomio cuadrado perfecto
• 141. Factorizar un trinomio cuadrado perfecto con fracciones
• 142. Factorización de una suma de cubos (x³ + y³)
• 143. Factorización de una diferencia de cubos (x³ - y³)
• 144. Factorización por agrupación
• 145. Factorización por agrupación│ejercicio 1
• 146. Factorización por agrupación│ejercicio 2

VI. Expresiones racionales

• 147. Simplificacion de fracciones algebraicas│ej 1 al 4
• 148. Simplificacion de fracciones algebraicas│ej 5 al 7
• 149. Simplificacion de fracciones algebraicas│ej 8
• 150. Simplificacion de fracciones algebraicas│ej 9
• 151. Simplificacion de fracciones algebraicas│ej 10
• 152. Simplificacion de fracciones algebraicas│ej 11
• 153. Simplificacion de fracciones algebraicas│ej 12
• 154. Expresión equivalente de una fracción algebraica
• 155. Suma de fracciones algebraicas│mismo denominador
• 156. Suma de fracciones algebraicas│ejercicio 1
• 157. Suma de fracciones algebraicas│ejercicio 2
• 158. Multiplicación de fracciones algebraicas
• 159. División de fracciones algebraicas
• 160. División de fracciones algebraicas│ejercicio 1
• 161. División de fracciones algebraicas│ejercicio 2
• 162. División de fracciones algebraicas │ejercicio 3

VII. Ecuaciones lineales

• 163. Concepto de ecuación
• 164. Identificar un elemento de una ecuación
• 165. Propiedades de transposición en una ecuación
• 166. Plantear una ecuación de primer grado│ejercicio 1
• 167. Plantear una ecuación de primer grado│ejercicio 2
• 168. Plantear una ecuación de primer grado│ejercicio 3
• 169. Principio de una ecuación lineal│ejercicio 1
• 170. Principio de una ecuación lineal│ejercicio 2
• 171. Despeje de una variable
• 172. Despeje de una variable│ejercicio 1
• 173. Despeje de una variable │ejercicio 2
• 174. Despeje de una variable│ejercicio 4
• 175. Despeje de una variable│ejercicio 3
• 176. Introducción a las ecuaciones de primer grado
• 177. Ecuaciones de primer grado
• 178. Ecuaciones de primer grado con paréntesis
• 179. Ecuaciones de primer grado con fracciones
• 180. Graficar funciones lineales
• 181. Graficar funciones lineales│ejercicio 1
• 182. Ecuaciones de primer grado│ejercicio 1
• 183. Ecuaciones de primer grado con fracciones│ej 1
• 184. Ecuaciones de primer grado con fracciones│ej 2
• 185. Ecuaciones de primer grado con fracciones│ej 3
• 186. Ecuaciones de primer grado con fracciones│ej 4
• 187. Ecuaciones de primer grado con fracciones│transposición
• 188. Plantear y resolver problemas de ecuaciones lineales
• 189. Ecuaciones de primer grado│problema 1
• 190. Ecuaciones de primer grado│problema 2
• 191. Ecuaciones de primer grado│problema 3
• 192. Ecuaciones de primer grado│problema 4
• 193. Ecuaciones de primer grado│problema 5
• 194. Ecuaciones de primer grado con fracciones│problema 1
• 195. Ecuaciones de primer grado con fracciones│problema 2
• 196. Ecuaciones de primer grado con fracciones│problema 3
• 197. Ecuaciones de primer grado con fracciones│problema 4
• 198. Ecuaciones de primer grado con fracciones│problema 5
• 199. Ecuaciones de primer grado con fracciones│problema 6
• 200. Ecuaciones de primer grado con fracciones│problema 7
• 201. Resolver una proporción de fracciones algebraicas
• 202. Ejercicios de ecuaciones de primer grado│compilado 1
• 203. Ejercicios de ecuaciones de primer grado│compilado 2
• 204. Convertir grados Fahrenheit a Centígrados

VIII. Ecuaciones simultáneas lineales 2x2

• 205. Intro a las ecuaciones simultáneas lineales 2x2
• 206. Plantear un sistema de ecuaciones 2x2
• 207. Identificar el método utilizado en un sistema 2x2
• 208. Convertir un sistema lineal 2x2 de fracciones a enteros
• 209. Sistema de ecuaciones lineales 2x2 │ Reducción
• 210. Sistemas de ecuaciones 2x2│método de eliminación 1
• 211. Sistemas de ecuaciones 2x2│método de eliminación 2
• 212. Sistemas de ecuaciones 2x2│método de eliminación 3
• 213. Sistemas 2x2 por método de eliminación│prob 1
• 214. Sistemas 2x2 por método de eliminación│prob 2
• 215. Sistemas 2x2 por método de eliminación│prob 3
• 216. Sistemas de ecuaciones 2x2 │ método de redución │ prob 4
• 217. Sistemas de ecuaciones 2x2│método de sustitución
• 218. Sistemas de ecuaciones 2x2│método de sustitución│prob 1
• 219. Sistemas de ecuaciones 2x2│método de sustitución│prob 2
• 220. Sistemas de ecuaciones 2x2│método de sustitución│prob 3
• 221. Sistemas de ecuaciones 2x2│método de sustitución│prob 4
• 222. Sistemas de ecuaciones 2x2│método de sustitución│prob 5
• 223. Sistemas de ecuaciones 2x2│método de sustitución│prob 6
• 224. Sistemas de ecuaciones 2x2│método de sustitución│prob 7
• 225. Sistemas de ecuaciones 2x2│método de igualación
• 226. Sistemas de ecuaciones 2x2│método de gráfico
• 227. Sistemas de ecuaciones 2x2│método de gráfico especial
• 228. Sistemas de ecuaciones 2x2│método de gráfico│problema
• 229. Sistemas de ecuaciones 2x2│método de gráfico│ejercicio
• 230. Sistemas de ecuaciones 2x2│método por determinantes
• 231. Problemas que generan un sistema de ecuaciones 2x2

IX. Ecuaciones simultáneas lineales 3x3

• 232. Sistemas de ecuaciones 3x3│método por determinantes
• 233. Sistemas de ecuaciones 3x3│método de eliminación
• 234. Sistemas de ecuaciones 3x3│método de igualación
• 235. Obtener un determinante de un sistema 3x3
• 236. Hallar un determinante de un sistema 3x3
• 237. Aplicación de los sistemas lineales 3x3

X. Ecuaciones cuadráticas

• 238. Tipos de ecuaciones cuadráticas│pura, mixta, completa
• 239. Intro a las ecuaciones cuadráticas│segundo grado
• 240. Discriminante de una ecuación cuadrática
• 241. Discriminante de una ecuación cuadrática│ejercicio 1
• 242. Discriminante de una ecuación cuadrática│ejercicio 2
• 243. Discriminante de una ecuación cuadrática│ejercicio 3
• 244. Intersecciones de una ecuación cuadrática│corto
• 245. ¿Por qué una ecuación cuadrática se iguala a cero?
• 246. Ecuaciones cuadráticas puras
• 247. Ecuaciones cuadráticas puras│ejercicio 1
• 248. Ecuaciones cuadráticas mixtas│compilado 1
• 249. Ecuaciones cuadráticas mixtas│compilado 2
• 250. Ecuaciones cuadráticas mixtas con fracciones
• 251. Ecuaciones cuadráticas completas
• 252. Identificar una ecuación cuadrática completa
• 253. Ecuaciones cuadráticas completas│ejercicio 1
• 254. Demostración de la fórmula general
• 255. Sustituir valores en la formula general
• 256. Ecuaciones cuadráticas por fórmula general
• 257. Ecuaciones cuadráticas por fórmula general│ej 1
• 258. Ecuaciones cuadráticas por fórmula general│ej 2
• 259. Radicalizar el resultado de una fórmula general
• 260. Ecuaciones cuadráticas con fracciones
• 261. Factorizar siempre un trinomio ax^2+bx+c
• 262. Hallar la ecuación cuadrática│dadas sus raíces
• 263. Ecuaciones cuadráticas por factorización│ej 1
• 264. Ecuaciones cuadráticas por factorización│ej 2
• 265. Ecuaciones cuadráticas por factorización│compilado
• 266. Ecuaciones cuadráticas completando el TCP│ej 1
• 267. Ecuaciones cuadráticas completando el TCP│ej 2
• 268. Número de intersecciones de una ecuación cuadrática│largo
• 269. Ecuaciones cuadráticas por método de gráfico
• 270. Ecuaciones cuadráticas por método de gráfico│problema 1
• 271. Aplicación de la función cuadrática
• 272. Ecuaciones cuadráticas│compilado de problemas
• 273. Ecuaciones cuadráticas│problema 1
• 274. Ecuaciones cuadráticas│problema 2
• 275. Ecuaciones cuadráticas│problema 3
• 276. Ecuaciones cuadráticas│problema 4
• 277. Ecuaciones cuadráticas│problema 5
• 278. Ecuaciones cuadráticas│problema 6
• 279. Ecuaciones cuadráticas│problema 7
• 280. Ecuaciones cuadráticas con Pitágoras
• 281. Problema de una ecuación cuadrática│difícil 1
• 282. Problema de una ecuación cuadrática│difícil 2

XI. Radicación

• 283. Radicación de números enteros│compilado
• 284. Radicación de números enteros│ejercicio 1
• 285. Radicación de un número│exponente fraccionario
• 286. Radicación de expresiones algebraicas│compilado
• 287. Radicación de expresiones algebraicas│ejercicio 1
• 288. Radicación de expresiones algebraicas│ejercicio 2
• 289. Radicación de expresiones algebraicas │ejercicio 3
• 290. Suma y resta de radicales
• 291. Factorizar suma de raíces
• 292. Radicación de fracciones│compilado
• 293. Radicación de fracciones│ejercicio 1
• 294. Racionalización del denominador│monomio
• 295. Racionalización del denominador│binomio
• 296. Racionalización del denominador│ejercicio 1
• 297. Racionalización del denominador│ejercicio 2

XII. Ecuaciones con radicales

• 298. Ecuaciones con radicales │ejercicio 1
• 299. Ecuaciones con radicales│ejercicio 4
• 300. Ecuaciones con raíz cuadrada
• 301. Ecuaciones con raíz cuadrada│problema

XIII. Inecuaciones (desigualdades)

• 302. Introducción a las desigualdades
• 303. Operaciones que no satisfacen una desigualdad
• 304. Desigualdad con 3 variables
• 305. Desigualdad lineal con una constante│ej 1
• 306. Desigualdad lineal con gráfica│ej 1
• 307. Desigualdad lineal con una constante│ej 2
• 308. Desigualdad lineal con gráfica│ej 2
• 309. Desigualdad lineal racional│ejercicio 1
• 310. Desigualdad lineal racional│ejercicio 2
• 311. Desigualdad lineal con tres componentes│ej 1
• 312. Desigualdad lineal con tres componentes│ej 2
• 313. Desigualdad lineal con valor absoluto│ejercicio 1
• 314. Desigualdad lineal con fracciones│ejercicio 1
• 315. Desigualdad lineal con fracciones│ejercicio 2
• 316. Desigualdad cúbica

XIV. 5 errores típicos en álgebra

• 317. 5 errores comunes en álgebra

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