Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Exercises - Page 134: 34


$\dfrac{(x-1)(x-7)}{x^{3/2}}$ or $\dfrac{(x-1)(x-7)}{\sqrt{x^{3}}}$ or $x^{-3/2}(x-1)(x-7)$

Work Step by Step

$7x^{-3/2}-8x^{-1/2}+x^{1/2}$ Take out common factor $x^{-3/2}$: $7x^{-3/2}-8x^{-1/2}+x^{1/2}=x^{-3/2}(7-8x+x^{2})=...$ Rearrange: $...=x^{-3/2}(x^{2}-8x+7)=...$ Factor the expression inside the parentheses: $...=x^{-3/2}(x-1)(x-7)=...$ Rearrange again: $...=\dfrac{(x-1)(x-7)}{x^{3/2}}$
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