Answer
$-\dfrac{1}{x(x+h)}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{1}{x+h}-\dfrac{1}{x}}{h}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{x(1)-(x+h)(1)}{x(x+h)}}{h}
\\\\=
\dfrac{x(1)-(x+h)(1)}{x(x+h)}\div h
\\\\=
\dfrac{x(1)-(x+h)(1)}{x(x+h)}\cdot\dfrac{1}{h}
\\\\=
\dfrac{x(1)-(x+h)(1)}{xh(x+h)}
\\\\=
\dfrac{x-x-h}{xh(x+h)}
\\\\=
\dfrac{-h}{xh(x+h)}
\\\\=
\dfrac{-\cancel{h}}{x\cancel{h}(x+h)}
\\\\=
-\dfrac{1}{x(x+h)}
.\end{array}
