Chapter 11 - Polynomial and Rational Functions - 11.4 Rational Functions - Exercises and Problems for Section 11.4 - Skill Refresher - Page 461: S5

$$\frac{-18x^2+18x+41}{\left(x-2\right)^2\left(x+1\right)}$$

Using the rules of fractions, we find: $$\frac{5}{\left(x-2\right)^2\left(x+1\right)}-\frac{18}{x-2} \\ \frac{5-18\left(x-2\right)\left(x+1\right)}{\left(x-2\right)^2\left(x+1\right)} \\ \frac{-18x^2+18x+41}{\left(x-2\right)^2\left(x+1\right)}$$