A/(x+1)+B/(x-1)=(x-3)/(x+1)(x-1)
左右同乘以(x+1)(x-1),得
A(x-1)+B(x+1)=x-3
(A+B)x-(A-B)=x-3
解方程组
A+B=1
A-B=3
得A=2,B=-1