Answer
$- \displaystyle \frac{20}{(x+h-4)(x-4)}$
Work Step by Step
$f(x)=\displaystyle \frac{5x}{x-4}$
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{1}{h}\cdot (\frac{5(x+h)}{x+h-4}-\frac{5x}{x-4})$
... LCD=$(x+h-4)(x-4)$
$=\displaystyle \frac{1}{h}\cdot\frac{5(x+h)(x-4)-5x(x-4+h)}{(x+h-4)(x-4)}$
$=\displaystyle \frac{1}{h}\cdot \frac{5x^{2}-20x+5hx-20h-5x^{2}+20x-5xh}{(x+h-4)(x-4)}$
$=\displaystyle \frac{1}{h}\cdot \frac{-20h}{(x+h-4)(x-4)}$ ... h cancels
$=- \displaystyle \frac{20}{(x+h-4)(x-4)}$
