Precalculus (6th Edition) Blitzer

The simplified form of the expression $\frac{3}{x-4}-\frac{2}{x+2}$ is $\frac{x+14}{{{x}^{2}}-6x+8}$.
Let us consider the expression $\frac{3}{x-4}-\frac{2}{x+2}$ And simplify: \begin{align} & \frac{3}{x-4}-\frac{2}{x+2}=\frac{3\left( x+2 \right)-2\left( x-4 \right)}{\left( x-2 \right)\left( x-4 \right)} \\ & =\frac{3x+6-2x+8}{{{x}^{2}}-6x+8} \\ & =\frac{x+14}{{{x}^{2}}-6x+8} \end{align} Therefore, $\frac{3}{x-4}-\frac{2}{x+2}=\frac{x+14}{{{x}^{2}}-6x+8}$ Thus, the simplified form of the expression $\frac{3}{x-4}-\frac{2}{x+2}$ is $\frac{x+14}{{{x}^{2}}-6x+8}$.