I'm only just now learning about partial fractions to solve integrals. I've read that
$$\frac{f(x)}{(px^2+qx+r)(x-a)}\equiv \frac{Ax+B}{(px^2+qx+r)}+\frac{C}{(x-a)}$$
I haven't figured out how it was decided that $Ax+B$ ought to be used and why it works. Can someone explain it?