已知x²+2 / x(x+1)(x+2) = A/x + B/x+1 + C/x+2 ,求A,B,C的值

已知x²+2 / x(x+1)(x+2) = A/x + B/x+1 + C/x+2 ,求A,B,C的值
已知x²+2 / x(x+1)(x+2) = A/x + B/x+1 + C/x+2 ,求A,B,C的值

已知x²+2 / x(x+1)(x+2) = A/x + B/x+1 + C/x+2 ,求A,B,C的值
A/x+B/(x+1)+C/(x+2)
=[A(x+1)(x+2)+Bx(x+2)+Cx(x+1)]/[x(x+1)(x+2)]
=[(A+B+C)x^2+(2A+2B+C+1)x+2A]/[x(x+1)(x+2)]
=(x^2+2)/[x(x+1)(x+2)]
对比,得
A+B+C=1
2A+2B+C=0
2A=2
解得A=1 B=-2 C=2