Chapter 6.4, Problem 7E

Matching In Exercises 5-8, match the rational expression with the form of its decomposition. [The decompositions are labeled (a), (b), (c), and (d).]

$\begin{array}{l}\left(\text{a}\right)\frac{A}{x}+\frac{B}{x+2}+\frac{C}{x-2}\left(\text{b}\right)\frac{A}{x}+\frac{B}{\begin{array}{l}x-4\\ \end{array}}\\ \left(\text{c}\right)\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-4}\left(\text{d}\right)\frac{A}{x}+\frac{B}{x-4}+\frac{C}{{\left(x-4\right)}^2}\end{array}$

$\frac{3x-1}{x{\left(x-4\right)}^2}$