$\frac{A}{x-1} + \frac{B}{x+2} + \frac{C}{(x+2)^2}$

$\frac{A}{x-1} + \frac{Bx+C}{(x+2)^2}$

$\frac{A}{x-1} + \frac{B}{x+2} + \frac{Cx+D}{(x+2)^2}$

$\frac{A}{x-1} + \frac{B}{(x+2)^2}$