Answer
$\frac{1}{x-3}$.
Work Step by Step
The given expression is
$=\frac{\frac{1}{x-2}}{1-\frac{1}{x-2}}$
Multiply the numerator and the denominator by $(x-2)$.
$=\frac{(x-2)}{(x-2)}\cdot \frac{\frac{1}{x-2}}{1-\frac{1}{x-2}}$
Use the distributive property.
$=\frac{(x-2)\cdot\frac{1}{x-2}}{(x-2)\cdot (1)-(x-2)\cdot \frac{1}{x-2}}$
Simplify.
$=\frac{1}{x-2-1}$
$=\frac{1}{x-3}$.
