College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5 - Page 75: 100

Answer

$\frac{(x^{2}+4)}{(x^{2}+3)^{5/3}}$

Work Step by Step

$(x^{2}+3)^{-2/3}+(x^{2}+3)^{-5/3}$ The greatest common factor of $(x^{2}+3)^{-2/3}+(x^{2}+3)^{-5/3}$ is $(x^{2}+3)$ with the smaller exponent in the two terms. Thus the greatest common factor is $(x^{2}+3)^{-5/3}$ Express each term as the product of greatest common factor and its other factor. $=(x^{2}+3)^{1}(x^{2}+3)^{-5/3}+(x^{2}+3)^{-5/3}$ $[(x^{2}+3)^{1}(x^{2}+3)^{-5/3}=(x^{2}+3)^{1-5/3} = (x^{2}+3)^{-2/3} ]$ Factor out the Greatest common factor. $=(x^{2}+3)^{-5/3}((x^{2}+3)+1)$ $=(x^{2}+3)^{-5/3}(x^{2}+3+1)$ $=(x^{2}+3)^{-5/3}(x^{2}+4)$ $=\frac{(x^{2}+4)}{(x^{2}+3)^{5/3}}$ [Because $a^{-1/m} = \frac{1}{a^{1/m}}]$
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