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: 93

Answer

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

Work Step by Step

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