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: 87

Answer

$\frac{2(\sqrt{7}-\sqrt{2})}{5}$

Work Step by Step

We simplify the fraction by multiplying through by $\sqrt{2}-\sqrt{7}$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{2}{\sqrt{2}+\sqrt{7}}=\frac{2}{\sqrt{2}+\sqrt{7}} \displaystyle \frac{\sqrt{2}-\sqrt{7}}{\sqrt{2}-\sqrt{7}}=\frac{2(\sqrt{2}-\sqrt{7})}{2-7}=\frac{2(\sqrt{2}-\sqrt{7})}{-5}=\frac{2(\sqrt{7}-\sqrt{2})}{5}$
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