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: 33

Answer

$\dfrac{-7}{\sqrt{x}-3}=-\dfrac{7(\sqrt{x}+3)}{x-9}$

Work Step by Step

$\dfrac{-7}{\sqrt{x}-3}$ Multiply the numerator and the denominator by the conjugate of the denominator and simplify: $\dfrac{-7}{\sqrt{x}-3}=\dfrac{-7}{-3+\sqrt{x}}\cdot\dfrac{-3-\sqrt{x}}{-3-\sqrt{x}}=\dfrac{-7(-3-\sqrt{x})}{(-3)^{2}-(\sqrt{x})^{2}}=...$ $...=\dfrac{-7(-3-\sqrt{x})}{9-x}=\dfrac{7(\sqrt{x}+3)}{9-x}=-\dfrac{7(\sqrt{x}+3)}{x-9}$
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