(2x+3)/x(x-1)(x+2)=A/x+B/(x-1)+C/(x+2)=(A(x-1)(x+2)+Bx(x+2)+Cx(x-1))/x(x-1)(x+2)即:(2x+3)/x(x-1)(x+2)=((A+B+C)x^2+(A+2B-C)x-2A)/x(x-1)(x+2)比较分子同次项系数得:A+B+C=0A+2B-C=2-2A=3联立上面三个方程求解,得:A=-3/2 B=5/3 C=-1/6