College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.6 - Factoring - P.6 Exercises: 114

Answer

$\displaystyle\frac{3x+2}{\sqrt{x}\sqrt{3x+4}}$

Work Step by Step

Factor out $x$ and $3x+4$: $\displaystyle \frac{1}{2}x^{-1/2}(3x+4)^{1/2}+\frac{3}{2}x^{1/2}(3x+4)^{-1/2}=\frac{1}{2}x^{-1/2}(3x+4)^{-1/2}[(3x+4)+3x]=\frac{1}{2}x^{-1/2}(3x+4)^{-1/2}(6x+4) =x^{-1/2}(3x+4)^{-1/2}(3x+2)=\frac{3x+2}{\sqrt{x}\sqrt{3x+4}}$
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