Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 44: 83

Answer

$\dfrac{3(1+x)^{1/3}-x(1+x)^{-2/3}}{(1+x)^{2/3}}=\dfrac{2x+3}{(1+x)^{4/3}}$

Work Step by Step

$\dfrac{3(1+x)^{1/3}-x(1+x)^{-2/3}}{(1+x)^{2/3}}$ Take out common factor $(1+x)^{-2/3}$ from the numerator and simplify: $\dfrac{3(1+x)^{1/3}-x(1+x)^{-2/3}}{(1+x)^{2/3}}=\dfrac{(1+x)^{-2/3}[3(1+x)^{3/3}-x]}{(1+x)^{2/3}}=...$ $...=\dfrac{(1+x)^{-2/3}(3+3x-x)}{(1+x)^{2/3}}=\dfrac{(1+x)^{-2/3}(2x+3)}{(1+x)^{2/3}}=...$ $...=\dfrac{2x+3}{(1+x)^{2/3}(1+x)^{2/3}}=\dfrac{2x+3}{(1+x)^{4/3}}$
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.