Answer
$1-\dfrac{1}{1-\dfrac{1}{x}}=\dfrac{1}{1-x}$
Work Step by Step
$1-\dfrac{1}{1-\dfrac{1}{x}}$
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:
$...=\dfrac{(x-1)-x}{x-1}=\dfrac{-1}{x-1}=\dfrac{1}{1-x}$
