Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Concept Check - Page 132: 15

Answer

The logical first step in rationalizing the denominator is to multiply by the conjugate. In this way we eliminate the possibility to have a square root in the denominator. CONJUGATE $$\frac{1-\sqrt x}{1-\sqrt x}$$

Work Step by Step

$\frac{3}{1+\sqrt x}$ The first logical step to rationalize the denominator is to multiply by the conjugate of the deniminator. CONJUGATE ${1-\sqrt x}$ $$(\frac{3}{1+\sqrt x})(\frac{1-\sqrt x}{1-\sqrt x})$$ $$\frac{3-3\sqrt x}{1-x}$$ $$\frac{3(1-\sqrt x)}{1-x}$$ Cancel similar terms Answer: 3
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