Solve x^2-6x-7/x^2-5x-50*x^2-18x+80/x^2-15x+56divx-1/x+5

$$\frac { x ^ { 2 } - 6 x - 7 } { x ^ { 2 } - 5 x - 50 } \times \frac { x ^ { 2 } - 18 x + 80 } { x ^ { 2 } - 15 x + 56 } \div \frac { x - 1 } { x + 5 }$$

Evaluate

$$\frac{x+1}{x-1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-18x+80}{x^{2}-15x+56}.

$$\frac{\frac{x^{2}-6x-7}{x^{2}-5x-50}\times \frac{\left(x-10\right)\left(x-8\right)}{\left(x-8\right)\left(x-7\right)}}{\frac{x-1}{x+5}}$$

Cancel out x-8 in both numerator and denominator.

$$\frac{\frac{x^{2}-6x-7}{x^{2}-5x-50}\times \frac{x-10}{x-7}}{\frac{x-1}{x+5}}$$

Multiply \frac{x^{2}-6x-7}{x^{2}-5x-50} times \frac{x-10}{x-7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{2}-6x-7\right)\left(x-10\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)}}{\frac{x-1}{x+5}}$$

Divide \frac{\left(x^{2}-6x-7\right)\left(x-10\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)} by \frac{x-1}{x+5} by multiplying \frac{\left(x^{2}-6x-7\right)\left(x-10\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)} by the reciprocal of \frac{x-1}{x+5}.

$$\frac{\left(x^{2}-6x-7\right)\left(x-10\right)\left(x+5\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)\left(x-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-10\right)\left(x-7\right)\left(x+1\right)\left(x+5\right)}{\left(x-10\right)\left(x-7\right)\left(x-1\right)\left(x+5\right)}$$

Cancel out \left(x-10\right)\left(x-7\right)\left(x+5\right) in both numerator and denominator.

$$\frac{x+1}{x-1}$$

Expand

$$\frac{x+1}{x-1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-18x+80}{x^{2}-15x+56}.

$$\frac{\frac{x^{2}-6x-7}{x^{2}-5x-50}\times \frac{\left(x-10\right)\left(x-8\right)}{\left(x-8\right)\left(x-7\right)}}{\frac{x-1}{x+5}}$$

Cancel out x-8 in both numerator and denominator.

$$\frac{\frac{x^{2}-6x-7}{x^{2}-5x-50}\times \frac{x-10}{x-7}}{\frac{x-1}{x+5}}$$

Multiply \frac{x^{2}-6x-7}{x^{2}-5x-50} times \frac{x-10}{x-7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{2}-6x-7\right)\left(x-10\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)}}{\frac{x-1}{x+5}}$$

Divide \frac{\left(x^{2}-6x-7\right)\left(x-10\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)} by \frac{x-1}{x+5} by multiplying \frac{\left(x^{2}-6x-7\right)\left(x-10\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)} by the reciprocal of \frac{x-1}{x+5}.

$$\frac{\left(x^{2}-6x-7\right)\left(x-10\right)\left(x+5\right)}{\left(x^{2}-5x-50\right)\left(x-7\right)\left(x-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-10\right)\left(x-7\right)\left(x+1\right)\left(x+5\right)}{\left(x-10\right)\left(x-7\right)\left(x-1\right)\left(x+5\right)}$$

Cancel out \left(x-10\right)\left(x-7\right)\left(x+5\right) in both numerator and denominator.

$$\frac{x+1}{x-1}$$