Find (A,B) such that (3x-27)/(x^2+3x-10) = A/(x-2) + B/(x+5).
you are looking for partial fractions here. there are several ways to do this. here's the easiest (i think):
multiply both sides by $\displaystyle (x - 2)(x + 5)$ to obtain
$\displaystyle 3x - 27 = A(x + 5) + B(x - 2)$ ............(1)
now, plug in $\displaystyle x = -5$ in equation (1) and solve for B
then plug in $\displaystyle x = 2$ in equation (1) and solve for A