初二下学期数学代数题已知 2x+3/x(x-1)(x+2)=a/x+b/(x-1)+c/(x+2)求a,b,c的值

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 23:09:41

初二下学期数学代数题
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)
2x+3=A*(x-1)(x+2)+B*x(x+2)+C*x(x-1)
2x+3=A(x^2+x-2)+B(x^2+2x)+C(x^2-x)
2x+3=(A+B+C)x^2+(A+2B-C)x-2A
A+B+C=0
A+2B-C=2
-2A=3
解方程组得：
A=-3/2,B=5/3,C=-1/6

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