Solve x^2-2x-8/x^2-13x-30-2x+4/x^2-13x-30

$$\frac { x ^ { 2 } - 2 x - 8 } { x ^ { 2 } - 13 x - 30 } - \frac { 2 x + 4 } { x ^ { 2 } - 13 x - 30 }$$

Evaluate

$$\frac{x-6}{x-15}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{x^{2}-13x-30}.

$$\frac{\left(x-4\right)\left(x+2\right)}{\left(x-15\right)\left(x+2\right)}-\frac{2x+4}{x^{2}-13x-30}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-4}{x-15}-\frac{2x+4}{x^{2}-13x-30}$$

Factor the expressions that are not already factored in \frac{2x+4}{x^{2}-13x-30}.

$$\frac{x-4}{x-15}-\frac{2\left(x+2\right)}{\left(x-15\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-4}{x-15}-\frac{2}{x-15}$$

Since \frac{x-4}{x-15} and \frac{2}{x-15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-4-2}{x-15}$$

Combine like terms in x-4-2.

$$\frac{x-6}{x-15}$$

Expand

$$\frac{x-6}{x-15}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{x^{2}-13x-30}.

$$\frac{\left(x-4\right)\left(x+2\right)}{\left(x-15\right)\left(x+2\right)}-\frac{2x+4}{x^{2}-13x-30}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-4}{x-15}-\frac{2x+4}{x^{2}-13x-30}$$

Factor the expressions that are not already factored in \frac{2x+4}{x^{2}-13x-30}.

$$\frac{x-4}{x-15}-\frac{2\left(x+2\right)}{\left(x-15\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-4}{x-15}-\frac{2}{x-15}$$

Since \frac{x-4}{x-15} and \frac{2}{x-15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-4-2}{x-15}$$

Combine like terms in x-4-2.

$$\frac{x-6}{x-15}$$