2x+3/x(x-1)(x+2)=A/B+B/x-1+C/x+2(A.B.C是常数）,求A.B.C的值

2x+3/x(x-1)(x+2)=A/B+B/x-1+C/x+2(A.B.C是常数）,求A.B.C的值
2x+3/x(x-1)(x+2)=A/B+B/x-1+C/x+2(A.B.C是常数）,求A.B.C的值

2x+3/x(x-1)(x+2)=A/B+B/x-1+C/x+2(A.B.C是常数）,求A.B.C的值
(2x+3)/[x(x-1)(x+2)]=A/x+B/(x-1)+C/(x+2)
=[A(x^2+x-2)+B(x^2+2x)+C(x^2-x)]/[x(x-1)(x+2)]
=[(A+B+C)x^2+(A+2B-C)x-2A]/[x(x-1)(x+2)]
可得:
A+B+C=0
A+2B-C=2
-2A=3
A=-3/2
B=5/3
C=-1/6