Chapter 6.6, Problem 58E

Match the rational expression on the left with the correct partial fraction decomposition form on the right.

$\mathit{ }\frac{x^2-2x+3}{x^2(x-4){(x}^2+5)}$

a. $\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x^4}+\frac{E}{x-4}+\frac{Fx+G}{x^2+5}$ b. $\frac{A}{x}+\frac{B}{x-4}+\frac{C}{{\left(x-4\right)}^2}+\frac{D}{{\left(x-4\right)}^3}+\frac{Fx+G}{x^2+5}+\frac{Hx+I}{{{(x}^2+5)}^2}$ c. $\mathit{ }\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-4}+\frac{D{x}^2+Ex+F}{x^3+5}$ d. $\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x-4}+\frac{E}{{(x-4)}^2}+\frac{Fx+G}{x^2+5}$ e. $\frac{A}{x}+\frac{B}{x-4}+\frac{Cx+D}{x^2+5}$ f. $\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-4}+\frac{Dx+E}{x^2+5}$