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: 89

Answer

$\frac{y\sqrt{3}-y\sqrt{y}}{3-y}$

Work Step by Step

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