Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 68

Answer

$\dfrac{a-4\sqrt{a}+3}{a-1}$

Work Step by Step

Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $ \dfrac{\sqrt{a}-3}{\sqrt{a}+1} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt{a}-3}{\sqrt{a}+1}\cdot\dfrac{\sqrt{a}-1}{\sqrt{a}-1} \\\\= \dfrac{\sqrt{a}(\sqrt{a})+\sqrt{a}(-1)-3(\sqrt{a})-3(-1)}{(\sqrt{a})^2-(1)^2} \\\\= \dfrac{a-1\sqrt{a}-3\sqrt{a}+3}{a-1} \\\\= \dfrac{a-4\sqrt{a}+3}{a-1} .\end{array}
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