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: 88

Answer

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

Work Step by Step

We simplify the fraction by multiplying through by $\sqrt{x}-1$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{1}{\sqrt{x}+1}=\frac{1}{\sqrt{x}+1} \displaystyle *\frac{\sqrt{x}-1}{\sqrt{x}-1}=\frac{\sqrt{x}-1}{x-1}$
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