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: 93



Work Step by Step

$x^{-3/2}+2x^{-1/2}+x^{1/2}$ Take out common factor $x^{-3/2}$: $x^{-3/2}+2x^{-1/2}+x^{1/2}=x^{-3/2}(1+2x+x^{4/2})=...$ $...=\dfrac{1}{\sqrt{x^{3}}}(x^{2}+2x+1)=...$ Factor the expression inside the parentheses, which is a perfect square trinomial: $...=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$
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