Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set: 44

Answer

$\dfrac{-8}{\sqrt{y}+4}=-\dfrac{8(\sqrt{y}-4)}{y-16}$

Work Step by Step

$\dfrac{-8}{\sqrt{y}+4}$ Multiply the numerator and the denominator by the conjugate of the denominator and simplify: $\dfrac{-8}{\sqrt{y}+4}=\dfrac{-8}{\sqrt{y}+4}\cdot\dfrac{\sqrt{y}-4}{\sqrt{y}-4}=\dfrac{-8(\sqrt{y}-4)}{(\sqrt{y})^{2}-4^{2}}=...$ $...=-\dfrac{8(\sqrt{y}-4)}{y-16}$
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