Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.4 Factoring Perfect-Square Trinomials and Differences of Squares - 5.4 Exercise Set: 108

Answer

$\left( x+\dfrac{1}{x} \right)\left( x-\dfrac{1}{x} \right)$

Work Step by Step

Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the given expression, $ x^2-\left( \dfrac{1}{x} \right)^2 ,$ is \begin{array}{l} \left( x+\dfrac{1}{x} \right)\left( x-\dfrac{1}{x} \right) \end{array}
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