Chapter 11 - Polynomial and Rational Functions - 11.4 Rational Functions - Exercises and Problems for Section 11.4 - Skill Refresher - Page 461: S9

$$\frac{1}{x-1}$$

Using the rules of fractions, we find: $$\frac{x^{-1}+x^{-2}}{1-x^{-2}} \\ \frac{x+1}{x^2\left(-\frac{1}{x^2}+1\right)} \\ \frac{x+1}{x^2-1} \\ \frac{x+1}{\left(x+1\right)\left(x-1\right)} \\ \frac{1}{x-1}$$