Answer
$\frac{1}{1-x}$
Work Step by Step
We form a common denominator for the bottom fractions, add, and take the reciprocal. Then we combine both fractions and simplify:
$1-\displaystyle \frac{1}{1-\frac{1}{x}}=1-\displaystyle \frac{1}{\frac{x}{x}-\frac{1}{x}}=1-\frac{x}{x-1}=\frac{x-1-x}{x-1}=$
$\displaystyle\frac{1}{1-x}$
