Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 44: 85



Work Step by Step

$\dfrac{1}{5-\sqrt{3}}$ Multiply both numerator and denominator by $5+\sqrt{3}$ and simplify: $\dfrac{1}{5-\sqrt{3}}=\Big(\dfrac{1}{5-\sqrt{3}}\Big)\Big(\dfrac{5+\sqrt{3}}{5+\sqrt{3}}\Big)=\dfrac{5+\sqrt{3}}{5^{2}-(\sqrt{3})^{2}}=...$ $...=\dfrac{5+\sqrt{3}}{25-3}=\dfrac{5+\sqrt{3}}{22}$
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