Answer
$\frac{-1}{2x(x+h)}$
Work Step by Step
$\frac{\frac{1}{2(x+h)}-\frac{1}{2x}}{h}=\frac{x-(x+h)}{2hx(x+h)}=\frac{-h}{2hx(x+h)}=$$\frac{-1}{2x(x+h)}$
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