Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises: 54

Answer

$9(6x+2)^{1/2}+3(9x-1)(6x+2)^{-1/2}=\dfrac{3(27x+5)}{(6x+2)^{1/2}}$

Work Step by Step

$9(6x+2)^{1/2}+3(9x-1)(6x+2)^{-1/2}$ Take out common factor $3(6x+2)^{-1/2}$ from the expression: $9(6x+2)^{1/2}+3(9x-1)(6x+2)^{-1/2}=...$ $...=3(6x+2)^{-1/2}[3(6x+2)+9x-1]=...$ Simplify the expression inside brackets: $...=3(6x+2)^{-1/2}(18x+6+9x-1)=...$ $...=3(6x+2)^{-1/2}(27x+5)=...$ Change the sign of the exponent of $6x+2$ by putting it as a denominator: $...=\dfrac{3(27x+5)}{(6x+2)^{1/2}}$
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