(2x-3)/(x-1)(x+2)=A/(x-1)+B/(x+2)
通分得：(2x-3)/(x-1)(x+2)=A(x+2)/(x-1)(x+2)+B(x-1)/(x-1)(x+2)
去分母得；2x-3=A(x+2)+B(x-1)
去括号得：2x-3=Ax+2A+Bx-B
整理得：2x-3=(A+B)x+2A-B
要使上面等式成立,则要满足：
A+B=2 2A-B=-3
解得：
A=-1/3 B=7/3