Resolver frac{x^{2}-x-2}{x^{2}-9}div(x^2-2x-3/3x^2-7x-6*3x^2-10x-8/x^2+x-12)

$$\frac { x ^ { 2 } - x - 2 } { x ^ { 2 } - 9 } \div ( \frac { x ^ { 2 } - 2 x - 3 } { 3 x ^ { 2 } - 7 x - 6 } \times \frac { 3 x ^ { 2 } - 10 x - 8 } { x ^ { 2 } + x - 12 } )$$

Calcular

$$\frac{\left(x-2\right)\left(x+4\right)}{\left(x-4\right)\left(x+3\right)}$$

Pasos de solución curta

Factoriza as expresións que aínda non o están en \frac{x^{2}-2x-3}{3x^{2}-7x-6}.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(3x+2\right)}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Anula x-3 no numerador e no denominador.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{x+1}{3x+2}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Multiplica \frac{x+1}{3x+2} por \frac{3x^{2}-10x-8}{x^{2}+x-12} mediante a multiplicación do numerador polo numerador e do denominador polo denominador.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)}}$$

Divide \frac{x^{2}-x-2}{x^{2}-9} entre \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)} mediante a multiplicación de \frac{x^{2}-x-2}{x^{2}-9} polo recíproco de \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)}.

$$\frac{\left(x^{2}-x-2\right)\left(3x+2\right)\left(x^{2}+x-12\right)}{\left(x^{2}-9\right)\left(x+1\right)\left(3x^{2}-10x-8\right)}$$

Factoriza as expresións que aínda non o están.

$$\frac{\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(x+4\right)\left(3x+2\right)}{\left(x-4\right)\left(x-3\right)\left(x+1\right)\left(x+3\right)\left(3x+2\right)}$$

Anula \left(x-3\right)\left(x+1\right)\left(3x+2\right) no numerador e no denominador.

$$\frac{\left(x-2\right)\left(x+4\right)}{\left(x-4\right)\left(x+3\right)}$$

Expande a expresión.

$$\frac{x^{2}+2x-8}{x^{2}-x-12}$$

Expandir

$$\frac{x^{2}+2x-8}{\left(x-4\right)\left(x+3\right)}$$

Pasos de solución curta

Factoriza as expresións que aínda non o están en \frac{x^{2}-2x-3}{3x^{2}-7x-6}.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(3x+2\right)}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Anula x-3 no numerador e no denominador.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{x+1}{3x+2}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Multiplica \frac{x+1}{3x+2} por \frac{3x^{2}-10x-8}{x^{2}+x-12} mediante a multiplicación do numerador polo numerador e do denominador polo denominador.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)}}$$

Divide \frac{x^{2}-x-2}{x^{2}-9} entre \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)} mediante a multiplicación de \frac{x^{2}-x-2}{x^{2}-9} polo recíproco de \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)}.

$$\frac{\left(x^{2}-x-2\right)\left(3x+2\right)\left(x^{2}+x-12\right)}{\left(x^{2}-9\right)\left(x+1\right)\left(3x^{2}-10x-8\right)}$$

Factoriza as expresións que aínda non o están.

$$\frac{\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(x+4\right)\left(3x+2\right)}{\left(x-4\right)\left(x-3\right)\left(x+1\right)\left(x+3\right)\left(3x+2\right)}$$

Anula \left(x-3\right)\left(x+1\right)\left(3x+2\right) no numerador e no denominador.

$$\frac{\left(x-2\right)\left(x+4\right)}{\left(x-4\right)\left(x+3\right)}$$

Expande a expresión.

$$\frac{x^{2}+2x-8}{x^{2}-x-12}$$