Answer
a) $\frac{A}{x-3} + \frac{B}{x+5}$
b) $\frac{A}{x-2} + \frac{B}{(x-2)^{2}} + \frac{Cx +D}{x^{2}+2}$
Work Step by Step
a) Assume that the degree of the numerator is less than the numerator by one.
$$\frac{A}{x-3} + \frac{B}{x+5}$$
b) Product of linear factors that are repeated
$$\frac{A}{x-2} + \frac{B}{(x-2)^{2}} + \frac{Cx +D}{x^{2}+2}$$
