Answer
$\displaystyle \frac{4x(x-1)}{(x+2)(x-2)},\qquad x\neq\pm 2$
Work Step by Step
We find the common denominator first.
Both denominators are linear, and they have no common factors, LCD=$(x+2)(x-2)$
Domain: $ x\neq\pm 2,$
We multiply each rational expression with 1 (either $\displaystyle \frac{x-2}{x-2}$ or $\displaystyle \frac{x+2}{x+2}$)
$\displaystyle \frac{3x}{x+2}\cdot\frac{x-2}{x-2}+\frac{x}{x-2}\cdot\frac{x+2}{x+2} = \frac{3x(x-2)+x(x+2)}{(x+2)(x-2)},\qquad x\neq\pm 2 $
$ = \displaystyle \frac{3x^{2}-6x+x^{2}+2x}{(x+2)(x-2)} ,\qquad x\neq\pm 2$
$ = \displaystyle \frac{4x^{2}-4x}{(x+2)(x-2)},\qquad x\neq\pm 2$
Factor out $4x $ in the numerator
$ = \displaystyle \frac{4x(x-1)}{(x+2)(x-2)},\qquad x\neq\pm 2$
There are no common factors to reduce further.
