A/x-2+B/x+1=3x/(x-2)(x+1),
(Ax+A+Bx-2B)/(x-2)(x+1)=3x/(x-2)(x+1),
[(A+B)x+(A-2B)]/(x-2)(x+1)=3x/(x-2)(x+1),
由恒等式得
A+B=3,A-2B=0
A=2,B=1
A/x-2+B/x+1=3x/(x-2)(x+1),
(Ax+A+Bx-2B)/(x-2)(x+1)=3x/(x-2)(x+1),
[(A+B)x+(A-2B)]/(x-2)(x+1)=3x/(x-2)(x+1),
由恒等式得
A+B=3,A-2B=0
A=2,B=1