Evaluate the integral of 4/(1-x)(1+x)^2. the answer is supposed to be -2/x+1 + ln |x+1/x-1|

I did A/1-x + B/1+x + C/1+x)^2 and eventually got this after multiplying by common denominators: -Bx^3+x^2(A-B)+x(2A+B-C)+A+B+C=1 and do not know how to solve for A, B, or C. Am I doing this right?