College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 71

Answer

$\frac{1}{1-x}$

Work Step by Step

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