## Precalculus: Mathematics for Calculus, 7th Edition

$1-\dfrac{1}{1-\dfrac{1}{x}}=\dfrac{1}{1-x}$
$1-\dfrac{1}{1-\dfrac{1}{x}}$ Evaluate the substraction in the denominator: $1-\dfrac{1}{1-\dfrac{1}{x}}=1-\dfrac{1}{\dfrac{x-1}{x}}=...$ Evaluate the division: $...=1-\dfrac{x}{x-1}=...$ Finally, evaluate the substraction and simplify: $...=\dfrac{(x-1)-x}{x-1}=\dfrac{-1}{x-1}=\dfrac{1}{1-x}$