Solve 3x+18/x^2+4x-12-x+6/x^2+4x-12

$$\frac{ 3x+18 }{ { x }^{ 2 } +4x-12 } - \frac{ x+6 }{ { x }^{ 2 } +4x-12 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x+18}{x^{2}+4x-12}.

$$\frac{3\left(x+6\right)}{\left(x-2\right)\left(x+6\right)}-\frac{x+6}{x^{2}+4x-12}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{3}{x-2}-\frac{x+6}{x^{2}+4x-12}$$

Factor the expressions that are not already factored in \frac{x+6}{x^{2}+4x-12}.

$$\frac{3}{x-2}-\frac{x+6}{\left(x-2\right)\left(x+6\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{3}{x-2}-\frac{1}{x-2}$$

Since \frac{3}{x-2} and \frac{1}{x-2} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 3 to get 2.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x+18}{x^{2}+4x-12}.

$$\frac{3\left(x+6\right)}{\left(x-2\right)\left(x+6\right)}-\frac{x+6}{x^{2}+4x-12}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{3}{x-2}-\frac{x+6}{x^{2}+4x-12}$$

Factor the expressions that are not already factored in \frac{x+6}{x^{2}+4x-12}.

$$\frac{3}{x-2}-\frac{x+6}{\left(x-2\right)\left(x+6\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{3}{x-2}-\frac{1}{x-2}$$

Since \frac{3}{x-2} and \frac{1}{x-2} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 3 to get 2.

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