Answer
$= -\frac{x-3}{x-2}$
Work Step by Step
$\frac{x-3}{x-6} \div \frac{x-2}{6-x}$
$= \frac{x-3}{x-6} \times \frac{6-x}{x-2}$
$= \frac{x-3}{x-6} \times \frac{-(x-6)}{x-2}$
$= \frac{x-3}{1} \times \frac{-1}{x-2}$
$= -\frac{x-3}{x-2}$
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