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: 92

Answer

$\frac{-1}{\sqrt{3}-\sqrt{5}}$

Work Step by Step

We simplify the fraction by multiplying through by $\sqrt{3}-\sqrt{5}$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{\sqrt{3}+\sqrt{5}}{2}=\frac{\sqrt{3}+\sqrt{5}}{2}*\displaystyle \frac{\sqrt{3}-\sqrt{5}}{\sqrt{3}-\sqrt{5}}=\frac{3-5}{2(\sqrt{3}-\sqrt{5})}=\frac{-2}{2(\sqrt{3}-\sqrt{5})}=\frac{-1}{\sqrt{3}-\sqrt{5}}$
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