Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.7 Radical Expressions - R.7 Exercises: 102

Answer

$\color{blue}{-\dfrac{\sqrt{21}+7}{4}}$

Work Step by Step

Rationalize the denominator by multiplying the conjugate of the denominator, which is $\sqrt3+\sqrt7$, to both the numerator and the denominator to obtain: $=\dfrac{\sqrt7(\sqrt3+\sqrt7)}{(\sqrt3-\sqrt7)(\sqrt3+\sqrt7)}$ Distribute $\sqrt7$ in the numerator and use the formula $(a-b)(a+b)=a^2-b^2$ to simplify the denominator to obtain: $=\dfrac{\sqrt{21}+\sqrt{49}}{(\sqrt3)^2-(\sqrt7)^2} \\=\dfrac{\sqrt{21}+7}{3-7} \\=\dfrac{\sqrt{21}+7}{-4} \\=\color{blue}{-\dfrac{\sqrt{21}+7}{4}}$
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