Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.1 - Rational Functions and Multiplying and Dividing Rational Expressions - Exercise Set - Page 348: 105

Answer

$\dfrac{1}{10y^{n+1}+30y}$

Work Step by Step

Factor the numerators and the denominators, when needed to have: $\\=\dfrac{y^{2n}+9}{10y} \cdot \dfrac{y^n-3}{(y^{2n}-9)(y^{2n}+9)} \\=\dfrac{y^{2n}+9}{10y} \cdot \dfrac{y^n-3}{(y^n-3)(y^n+3)(y^{2n}+9)}$ Cancel the common factors to have: $\require{cancel}\\=\dfrac{\cancel{y^{2n}+9}}{10y} \cdot \dfrac{\cancel{y^n-3}}{\cancel{(y^n-3)}(y^n+3)\cancel{(y^{2n}+9)}} \\=\dfrac{1}{10y(y^n+3)} \\=\dfrac{1}{10y^{n+1}+30y}$
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