Chapter 5 - Polynomials and Factoring - 5.4 Factoring Perfect-Square Trinomials and Differences of Squares - 5.4 Exercise Set - Page 333: 108

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

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}