Solve x^2-2x-8/x^2-5x-14*4x-28/x^2-9x+20

$$\frac { x ^ { 2 } - 2 x - 8 } { x ^ { 2 } - 5 x - 14 } \cdot \frac { 4 x - 28 } { x ^ { 2 } - 9 x + 20 }$$

Evaluate

$$\frac{4}{x-5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{x^{2}-5x-14}.

$$\frac{\left(x-4\right)\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}\times \frac{4x-28}{x^{2}-9x+20}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-4}{x-7}\times \frac{4x-28}{x^{2}-9x+20}$$

Multiply \frac{x-4}{x-7} times \frac{4x-28}{x^{2}-9x+20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(4x-28\right)}{\left(x-7\right)\left(x^{2}-9x+20\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(x-7\right)\left(x-4\right)}{\left(x-7\right)\left(x-5\right)\left(x-4\right)}$$

Cancel out \left(x-7\right)\left(x-4\right) in both numerator and denominator.

$$\frac{4}{x-5}$$

Expand

$$\frac{4}{x-5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{x^{2}-5x-14}.

$$\frac{\left(x-4\right)\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}\times \frac{4x-28}{x^{2}-9x+20}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-4}{x-7}\times \frac{4x-28}{x^{2}-9x+20}$$

Multiply \frac{x-4}{x-7} times \frac{4x-28}{x^{2}-9x+20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(4x-28\right)}{\left(x-7\right)\left(x^{2}-9x+20\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(x-7\right)\left(x-4\right)}{\left(x-7\right)\left(x-5\right)\left(x-4\right)}$$

Cancel out \left(x-7\right)\left(x-4\right) in both numerator and denominator.

$$\frac{4}{x-5}$$