Answer
$\frac{3}{x}; x \ne 0,2;$
Work Step by Step
$\frac{\frac{1}{x}- \frac{1}{2} }{\frac{1}{3} - \frac{x}{6}}$
Take LCD in numerator and denominator,
$= \frac{\frac{2-x}{2x}}{\frac{6-3x}{18}}$
$= \frac{\frac{2-x}{2x}}{\frac{3(2-x)}{18}} ; x \ne 0,2;$
$= \frac{2-x}{2x} \times \frac{18} {3(2-x)}; x \ne 0,2;$
Divide out common factors.
$= \frac{3}{x}; x \ne 0,2;$
