Solve x^2-6x-16/x^2+8x-9divx^2-12x+32/x^2+16x+63

$$\frac { x ^ { 2 } - 6 x - 16 } { x ^ { 2 } + 8 x - 9 } \div \frac { x ^ { 2 } - 12 x + 32 } { x ^ { 2 } + 16 x + 63 }$$

Evaluate

$$\frac{\left(x+2\right)\left(x+7\right)}{\left(x-4\right)\left(x-1\right)}$$

Short Solution Steps

Divide \frac{x^{2}-6x-16}{x^{2}+8x-9} by \frac{x^{2}-12x+32}{x^{2}+16x+63} by multiplying \frac{x^{2}-6x-16}{x^{2}+8x-9} by the reciprocal of \frac{x^{2}-12x+32}{x^{2}+16x+63}.

$$\frac{\left(x^{2}-6x-16\right)\left(x^{2}+16x+63\right)}{\left(x^{2}+8x-9\right)\left(x^{2}-12x+32\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-8\right)\left(x+2\right)\left(x+7\right)\left(x+9\right)}{\left(x-8\right)\left(x-4\right)\left(x-1\right)\left(x+9\right)}$$

Cancel out \left(x-8\right)\left(x+9\right) in both numerator and denominator.

$$\frac{\left(x+2\right)\left(x+7\right)}{\left(x-4\right)\left(x-1\right)}$$

Expand the expression.

$$\frac{x^{2}+9x+14}{x^{2}-5x+4}$$

Expand

$$\frac{x^{2}+9x+14}{\left(x-4\right)\left(x-1\right)}$$

Short Solution Steps

Divide \frac{x^{2}-6x-16}{x^{2}+8x-9} by \frac{x^{2}-12x+32}{x^{2}+16x+63} by multiplying \frac{x^{2}-6x-16}{x^{2}+8x-9} by the reciprocal of \frac{x^{2}-12x+32}{x^{2}+16x+63}.

$$\frac{\left(x^{2}-6x-16\right)\left(x^{2}+16x+63\right)}{\left(x^{2}+8x-9\right)\left(x^{2}-12x+32\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-8\right)\left(x+2\right)\left(x+7\right)\left(x+9\right)}{\left(x-8\right)\left(x-4\right)\left(x-1\right)\left(x+9\right)}$$

Cancel out \left(x-8\right)\left(x+9\right) in both numerator and denominator.

$$\frac{\left(x+2\right)\left(x+7\right)}{\left(x-4\right)\left(x-1\right)}$$

Expand the expression.

$$\frac{x^{2}+9x+14}{x^{2}-5x+4}$$