Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises: 96

Answer

$x^{-1/2}(x+1)^{1/2}+x^{1/2}(x+1)^{-1/2}=\dfrac{2x+1}{\sqrt{x(x+1)}}$

Work Step by Step

$x^{-1/2}(x+1)^{1/2}+x^{1/2}(x+1)^{-1/2}$ Take out common factor $x^{-1/2}(x+1)^{-1/2}$: $x^{-1/2}(x+1)^{-1/2}[(x+1)+x]=x^{-1/2}(x+1)^{-1/2}(2x+1)=...$ $...=\dfrac{2x+1}{x^{1/2}(x+1)^{1/2}}=\dfrac{2x+1}{\sqrt{x(x+1)}}$
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