Solve x^2-x-2/x^2+8x+15*x^2-2x-15/x^2+3x+2

$$\frac { x ^ { 2 } - x - 2 } { x ^ { 2 } + 8 x + 15 } \times \frac { x ^ { 2 } - 2 x - 15 } { x ^ { 2 } + 3 x + 2 }$$

Evaluate

$$\frac{\left(x-5\right)\left(x-2\right)}{\left(x+2\right)\left(x+5\right)}$$

Short Solution Steps

Multiply \frac{x^{2}-x-2}{x^{2}+8x+15} times \frac{x^{2}-2x-15}{x^{2}+3x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-x-2\right)\left(x^{2}-2x-15\right)}{\left(x^{2}+8x+15\right)\left(x^{2}+3x+2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x-2\right)\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+5\right)}$$

Cancel out \left(x+1\right)\left(x+3\right) in both numerator and denominator.

$$\frac{\left(x-5\right)\left(x-2\right)}{\left(x+2\right)\left(x+5\right)}$$

Expand the expression.

$$\frac{x^{2}-7x+10}{x^{2}+7x+10}$$

Expand

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

Short Solution Steps

Multiply \frac{x^{2}-x-2}{x^{2}+8x+15} times \frac{x^{2}-2x-15}{x^{2}+3x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-x-2\right)\left(x^{2}-2x-15\right)}{\left(x^{2}+8x+15\right)\left(x^{2}+3x+2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x-2\right)\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+5\right)}$$

Cancel out \left(x+1\right)\left(x+3\right) in both numerator and denominator.

$$\frac{\left(x-5\right)\left(x-2\right)}{\left(x+2\right)\left(x+5\right)}$$

Expand the expression.

$$\frac{x^{2}-7x+10}{x^{2}+7x+10}$$