Solve x^2+8x+15/x^2+x-6*x^2-12x+20/x^2-16x+60

$$\frac { x ^ { 2 } + 8 x + 15 } { x ^ { 2 } + x - 6 } \cdot \frac { x ^ { 2 } - 12 x + 20 } { x ^ { 2 } - 16 x + 60 }$$

Evaluate

$$\frac{x+5}{x-6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+8x+15}{x^{2}+x-6}.

$$\frac{\left(x+3\right)\left(x+5\right)}{\left(x-2\right)\left(x+3\right)}\times \frac{x^{2}-12x+20}{x^{2}-16x+60}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x+5}{x-2}\times \frac{x^{2}-12x+20}{x^{2}-16x+60}$$

Factor the expressions that are not already factored in \frac{x^{2}-12x+20}{x^{2}-16x+60}.

$$\frac{x+5}{x-2}\times \frac{\left(x-10\right)\left(x-2\right)}{\left(x-10\right)\left(x-6\right)}$$

Cancel out x-10 in both numerator and denominator.

$$\frac{x+5}{x-2}\times \frac{x-2}{x-6}$$

Multiply \frac{x+5}{x-2} times \frac{x-2}{x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+5\right)\left(x-2\right)}{\left(x-2\right)\left(x-6\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x+5}{x-6}$$

Expand

$$\frac{x+5}{x-6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+8x+15}{x^{2}+x-6}.

$$\frac{\left(x+3\right)\left(x+5\right)}{\left(x-2\right)\left(x+3\right)}\times \frac{x^{2}-12x+20}{x^{2}-16x+60}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x+5}{x-2}\times \frac{x^{2}-12x+20}{x^{2}-16x+60}$$

Factor the expressions that are not already factored in \frac{x^{2}-12x+20}{x^{2}-16x+60}.

$$\frac{x+5}{x-2}\times \frac{\left(x-10\right)\left(x-2\right)}{\left(x-10\right)\left(x-6\right)}$$

Cancel out x-10 in both numerator and denominator.

$$\frac{x+5}{x-2}\times \frac{x-2}{x-6}$$

Multiply \frac{x+5}{x-2} times \frac{x-2}{x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+5\right)\left(x-2\right)}{\left(x-2\right)\left(x-6\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x+5}{x-6}$$