Answer
$\frac{-1}{2x}$
Work Step by Step
We find a common denominator for the top fractions, then simplify:
$\displaystyle \frac{\frac{1}{x}-\frac{1}{2}}{x-2}=\frac{\frac{2}{2x}-\frac{x}{2x}}{x-2}=\frac{\frac{2-x}{2x}}{x-2}=\frac{2-x}{2x(x-2)}=\frac{2-x}{-2x(2-x)}=\frac{-1}{2x}$
