Answer
$\frac{3}{x}$, $x\ne0, 2$
Work Step by Step
Step 1. To remove the fractions, we can multiply both the numerator and the denominator with a common factor $6x$.
Step 2. We have $\frac{\frac{1}{x}-\frac{1}{2}}{\frac{1}{3}-\frac{x}{6}}\cdot \frac{6x}{6x}=\frac{6-3x}{2x-x^2}=\frac{3(2-x)}{x(2-x)}$
Step 3. Provided that $x\ne0, 2$, simplify the above result. We get $\frac{3}{x}$
Step 4. We conclude the result as $\frac{3}{x}$, with $x\ne0, 2$
