## College Algebra 7th Edition

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