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: 85

Answer

$\frac{5+\sqrt{3}}{22}$

Work Step by Step

We simplify the fraction by multiplying through by $5+\sqrt{3}$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{1}{5-\sqrt{3}}=\frac{1}{5-\sqrt{3}} \displaystyle \frac{5+\sqrt{3}}{5+\sqrt{3}}=\frac{5+\sqrt{3}}{25-3}=\frac{5+\sqrt{3}}{22}$
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