(-x+4)/[x(x-1)(x+2)]=A/x+B/(x-1)+C/(x+2)
就是右侧通分后是左侧的结果
A/x+B/(x-1)+C/(x+2)
通分
=[A(x-1)(x+2)+Bx(x+2)+Cx(x-1)]/[x(x-1)(x+2)]
=(Ax²+Ax-2A+Bx²+2Bx+Cx²-Cx)/[x(x-1)(x+2)]
=[(A+B+C)x²+(A+2B-C)x-2A]/[x(x-1)(x+2)]
=(-x+4)/[x(x-1)(x+2)]
分子分母都相等
所以A+B+C=0
A+2B-C=-1
-2A=4
所以
A=-2
所以
B+C=2
2B-C=1
解得
B=1,C=1