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