Answer
The simplified form of the expression $\frac{3}{x-4}-\frac{2}{x+2}$ is $\frac{x+14}{{{x}^{2}}-6x+8}$.
Work Step by Step
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 $\frac{x+14}{{{x}^{2}}-6x+8}$.
