If you get to (x^2+3x+4)/((x-2)^2(x-3)) = A/((x-2)^2) + B/(x-2) + C/(x-3), then you can say that (x^2 + 3x + 4) = A(x-3) + B(x-2) + C(x-2)^2.. then if you let x=2, the B and C terms will go to 0, allowing you to easily find A (14 = -A).. Once you have found A, you can expand the right hand side...