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: 101

Answer

$\dfrac{1}{x^n-4}$

Work Step by Step

The given expression can be written as: $\\=\dfrac{x^n+4}{(x^n)^2-4^2}$ RECALL: $a^2-b^2=(a-b)(a+b)$ Factor the denominator using the formula above where $a=x^n$ and $b=4$ to have: $\\=\dfrac{x^n+4}{(x^n-4)(x^n+4)}$ Cancel the common factors to have: $\\\require{cancel}=\dfrac{\cancel{x^n+4}}{(x^n-4)\cancel{(x^n+4)}} \\=\dfrac{1}{x^n-4}$
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