已知X×(X-1)×(X+2)分之2X+3等于X分之A加X-1分之B加X+2分之C的值

2024-12-26 09:39:26
推荐回答(1个)
回答1:

(2x+3)/x(x-1)(x+2)=A/x+B/(x-1)+C/(x+2)=(A(x-1)(x+2)+Bx(x+2)+Cx(x-1))/x(x-1)(x+2)
即:
(2x+3)/x(x-1)(x+2)=((A+B+C)x^2+(A+2B-C)x-2A)/x(x-1)(x+2)
比较分子同次项系数得:
A+B+C=0
A+2B-C=2
-2A=3
联立上面三个方程求解,得:A=-3/2 B=5/3 C=-1/6