The integral of 1/(x-3)(x+2)

The answer is 1/5 ln |x-2/x| + C

I split it up to be A/(x-3) + B/(x+2) = (Ax+2A+Bx-3B)/(x-3)(x+2) = (x(A+B)+2A-3B)/(x-3)(x+2). Then I set A+B = 0 so 2A-3B must equal 1? Am I doing this right? I don't exactly know where to start by solving for A or B. (Worried)

Thank you!