College Algebra 7th Edition

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

Chapter P, Prerequisites - Chapter P Review - Exercises: 89

Answer

$\displaystyle10+10\sqrt{2}$

Work Step by Step

We multiply the numerator and denominator by $\sqrt{2}+1$ and use the fact that $(a+b)(a-b)=a^2-b^2$ to simplify: $\displaystyle \frac{10}{\sqrt{2}-1}=\frac{10}{\sqrt{2}-1}\cdot\frac{\sqrt{2}+1}{\sqrt{2}+1}=\frac{10+10\sqrt{2}}{2-1}=10+10\sqrt{2}$
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