右边=[A(x-1)+B(x+1)]/(x+1)(x-1)
=[(A+B)x+(B-A)]/(x²-1)
=3x/(x²-1)
所以(A+B)x+(B-A)=3x
所以A+B=3
B-A=0
所以
A=3/2,B=3/2