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: 91

Answer

$\dfrac{1-\sqrt{5}}{3}=-\dfrac{4}{3+3\sqrt{5}}$

Work Step by Step

$\dfrac{1-\sqrt{5}}{3}$ Multiply both numerator and denominator by $1+\sqrt{5}$ and simplify: $\dfrac{1-\sqrt{5}}{3}=\Big(\dfrac{1-\sqrt{5}}{3}\Big)\Big(\dfrac{1+\sqrt{5}}{1+\sqrt{5}}\Big)=\dfrac{1^{2}-(\sqrt{5})^{2}}{3+3\sqrt{5}}=...$ $...=\dfrac{1-5}{3+3\sqrt{5}}=-\dfrac{4}{3+3\sqrt{5}}$
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