Answer
$x=13$
Work Step by Step
Multiply both sides by $x-5$:
$$3(x-5)+\frac{2}{x-5}(x-5)=\frac{2x}{x-5}(x-5)$$
$$3x-15+2=2x$$
$$3x-2x-15+2=0$$
$$x-13=0$$
$$x=13$$
Checking:
$$3+\frac{2}{13-5}\stackrel{?}{=}\frac{2(13)}{13-5}$$
$$3+\frac{1}{4}\stackrel{?}{=}\frac{26}{8}$$
$$\frac{12+1}{4}\stackrel{?}{=}\frac{13}{4}$$
$$\frac{13}{4}=\frac{13}{4}~True$$
Thus, the solution is $x=13$.
