College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 48: 65

Answer

$\dfrac{(-b+2)(1+b)}{b(1-b)}$

Work Step by Step

The given expression, $ \dfrac{1+\dfrac{1}{1-b}}{1-\dfrac{1}{1+b}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{(1-b)+1}{1-b}}{\dfrac{(1+b)-1}{1+b}} \\\\= \dfrac{\dfrac{-b+2}{1-b}}{\dfrac{b}{1+b}} \\\\= \dfrac{-b+2}{1-b}\div\dfrac{b}{1+b} \\\\= \dfrac{-b+2}{1-b}\cdot\dfrac{1+b}{b} \\\\= \dfrac{(-b+2)(1+b)}{b(1-b)} .\end{array}
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