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Fracciones algebraicas

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Fracciones algebraicas

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About this activity

Juego sobre fracciones algebraicas

Created by

VICTOR ACEITUNO
VICTOR ACEITUNO
Guatemala

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Fracciones algebraicas
 

Fracciones algebraicasOnline version

Juego sobre fracciones algebraicas

by VICTOR ACEITUNO
1

¿Qué es una fracción algebraica?

Una fracción algebraica es una expresión racional con polinómios en el numerador y el denominador. Se estudia para simplificar, factorizar y resolver ecuaciones.

2

Definición

La fracción algebraica tiene numerador y denominador polinomiales. Su dominio excluye los ceros del denominador para evitar divisiones por cero.

3

Dominio

Para cada fracción, el denominador no puede ser cero. Restringimos los valores de las variables donde el polinomio del denominador se anula.

4

Factorización

Factoriza tanto el numerador como el denominador para identificar factores comunes y simplificar la fracción de forma segura.

5

Simplificación

Si un factor común aparece en numerador y denominador, se elimina. Se obtiene una forma reducida equivalente.

6

Suma y resta

Para sumar o restar fracciones algebraicas, iguala denominadores y combina términos semejantes. Simplifica al final.

7

Suma y resta

Para sumar o restar fracciones algebraicas, iguala denominadores y combina términos semejantes. Simplifica al final.

8

Multiplicación

Multiplica numeradores entre sí y denominadores entre sí. Luego simplifica factores comunes antes de multiplicar o dividir.

9

División

Dividir por una fracción equivale a multiplicar por su recíproca. Invierte el numerador y denominador del divisor y multiplica.

10

Ejemplos

Ejemplo: (x^2 - 9)/(x^2 - 3x) se factoriza como (x-3)(x+3)/[x(x-3)]. Al eliminar (x-3), resulta (x+3)/x, con x ≠ 0, 3.

11

Aplicaciones

Las fracciones algebraicas aparecen en fracciones de funciones, ecuaciones racionales y problemas de tasas de cambio. La clave es la factorización y la reducción.
 
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