Solve x^2-12x+36/x^2-7x-8divx^2-36/x^2+14x+13

$$\frac { x ^ { 2 } - 12 x + 36 } { x ^ { 2 } - 7 x - 8 } \div \frac { x ^ { 2 } - 36 } { x ^ { 2 } + 14 x + 13 }$$

Evaluate

$$\frac{\left(x-6\right)\left(x+13\right)}{\left(x-8\right)\left(x+6\right)}$$

Short Solution Steps

Divide \frac{x^{2}-12x+36}{x^{2}-7x-8} by \frac{x^{2}-36}{x^{2}+14x+13} by multiplying \frac{x^{2}-12x+36}{x^{2}-7x-8} by the reciprocal of \frac{x^{2}-36}{x^{2}+14x+13}.

$$\frac{\left(x^{2}-12x+36\right)\left(x^{2}+14x+13\right)}{\left(x^{2}-7x-8\right)\left(x^{2}-36\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(x+13\right)\left(x-6\right)^{2}}{\left(x-8\right)\left(x-6\right)\left(x+1\right)\left(x+6\right)}$$

Cancel out \left(x-6\right)\left(x+1\right) in both numerator and denominator.

$$\frac{\left(x-6\right)\left(x+13\right)}{\left(x-8\right)\left(x+6\right)}$$

Expand the expression.

$$\frac{x^{2}+7x-78}{x^{2}-2x-48}$$

Expand

$$\frac{x^{2}+7x-78}{\left(x-8\right)\left(x+6\right)}$$

Short Solution Steps

Divide \frac{x^{2}-12x+36}{x^{2}-7x-8} by \frac{x^{2}-36}{x^{2}+14x+13} by multiplying \frac{x^{2}-12x+36}{x^{2}-7x-8} by the reciprocal of \frac{x^{2}-36}{x^{2}+14x+13}.

$$\frac{\left(x^{2}-12x+36\right)\left(x^{2}+14x+13\right)}{\left(x^{2}-7x-8\right)\left(x^{2}-36\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(x+13\right)\left(x-6\right)^{2}}{\left(x-8\right)\left(x-6\right)\left(x+1\right)\left(x+6\right)}$$

Cancel out \left(x-6\right)\left(x+1\right) in both numerator and denominator.

$$\frac{\left(x-6\right)\left(x+13\right)}{\left(x-8\right)\left(x+6\right)}$$

Expand the expression.

$$\frac{x^{2}+7x-78}{x^{2}-2x-48}$$