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

Answer

$x^{-3/2}+2x^{-1/2}+x^{1/2}=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$

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: $...=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.