已知 2x+3/x(x-1)(x+2)=a/x+b/(x-1)+c/(x+2)求a,b,c的值

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已知 2x+3/x(x-1)(x+2)=a/x+b/(x-1)+c/(x+2)求a,b,c的值
已知 2x+3/x(x-1)(x+2)=a/x+b/(x-1)+c/(x+2)求a,b,c的值

已知 2x+3/x(x-1)(x+2)=a/x+b/(x-1)+c/(x+2)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