如果x(x+1)(x+2)分之x的平方+2=x分之A加x+1分之B加x+2分之C,求A、B、C的值,

网友回答

(x²+2)/[x(x+1)(x+2)]=A/x+B/(x+1)+C/(x+2)
(x²+2)/[x(x+1)(x+2)]=[A(x+1)(x+2)]+Bx(x+2)+Cx(x+1)]/[x(x+1)(x+2)]
x²+2=A(x²+3x+2)+B(x²+2x)+C(x²+x)
x²+2=(A+B+C)x²+(3A+2B+C)x+2A
由此2A=2A+B+C=1
3A+2B+C=0
解得A=1,B=-3,C=3