Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 34

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