右边=[A(x+1)-B(x-2)]/(x-2)(x+1)
=[(A-B)x+(A+2B)]/(x²-x-2)
=(3x+4)/(x²-x-2)
所以(A-B)x+(A+2B)=3x+4
所以A-B=3
A+2B=4
A=10/3,B=1/3