Answer
$ \displaystyle \frac{6}{(x+h+3)(x+3)}$
Work Step by Step
$f(x)=\displaystyle \frac{2x}{x+3}$
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{1}{h}\cdot (\frac{2(x+h)}{x+h+3}-\frac{2x}{x+3})$
... LCD=$(x+h+3)(x+3)$
$=\displaystyle \frac{1}{h}\cdot\frac{2(x+h)(x+3)-2x(x+3+h)}{(x+h+3)(x+3)}$
$=\displaystyle \frac{1}{h}\cdot \frac{2x^{2}+6x+2hx+6h-2x^{2}-6x-2xh}{(x+h+3)(x+3)}$
$=\displaystyle \frac{1}{h}\cdot \frac{6h}{(x+h+3)(x+3)}$ ... h cancels
$= \displaystyle \frac{6}{(x+h+3)(x+3)}$
