Answer
$\displaystyle \frac{-1}{x(x+h)}$
Work Step by Step
First, simplify $\displaystyle \frac{1}{x+h}-\frac{1}{x}$
LCD = $x(x+h)$
$\displaystyle \frac{1}{x+h}\cdot\frac{x}{x}-\frac{1}{x}\cdot\frac{x+h}{x+h}=\frac{x-(x+h)}{x(x+h)}$
$=\displaystyle \frac{-h}{x(x+h)}$
Now,
$\displaystyle \frac{1}{h}\left(\frac{1}{x+h}-\frac{1}{x}\right)$=$\displaystyle \frac{1}{h}\left(\frac{-h}{x(x+h)}\right)$
... h cancels,
$=\displaystyle \frac{-1}{x(x+h)}$
