Solve x^2-6x/x^2-x-30-2x-12/x^2-x-30

$$\frac { x ^ { 2 } - 6 x } { x ^ { 2 } - x - 30 } - \frac { 2 x - 12 } { x ^ { 2 } - x - 30 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-6x}{x^{2}-x-30}.

$$\frac{x\left(x-6\right)}{\left(x-6\right)\left(x+5\right)}-\frac{2x-12}{x^{2}-x-30}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{x}{x+5}-\frac{2x-12}{x^{2}-x-30}$$

Factor the expressions that are not already factored in \frac{2x-12}{x^{2}-x-30}.

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

Cancel out x-6 in both numerator and denominator.

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

Since \frac{x}{x+5} and \frac{2}{x+5} have the same denominator, subtract them by subtracting their numerators.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-6x}{x^{2}-x-30}.

$$\frac{x\left(x-6\right)}{\left(x-6\right)\left(x+5\right)}-\frac{2x-12}{x^{2}-x-30}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{x}{x+5}-\frac{2x-12}{x^{2}-x-30}$$

Factor the expressions that are not already factored in \frac{2x-12}{x^{2}-x-30}.

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

Cancel out x-6 in both numerator and denominator.

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

Since \frac{x}{x+5} and \frac{2}{x+5} have the same denominator, subtract them by subtracting their numerators.

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