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: 86

Answer

$-6-3\sqrt{5}$

Work Step by Step

We simplify the fraction by multiplying through by $2+\sqrt{5}$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{3}{2-\sqrt{5}}=\frac{3(2+\sqrt{5})}{(2+\sqrt{5})(2-\sqrt{5})}=\frac{6+3\sqrt{5}}{4-5}=-6-3\sqrt{5}$
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