Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 71



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: $...=\dfrac{(x-1)-x}{x-1}=\dfrac{-1}{x-1}=\dfrac{1}{1-x}$
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