已知2x+3x(x?1)(x+2)＝Ax+Bx?1+Cx+2

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∵Ax+Bx?1+Cx+2
======以下答案可供参考======
供参考答案1:
左边=[2*(x-1)(x+2)+3]/x(x-1)(x+2)
=[(2x-2)(x+2)+3]/x(x-1)(x+2)
=(2x^2+2x-4+3)/x(x-1)(x+2)
右边=[A(x-1)(x+2)+Bx(x+2)+Cx(x-1)]/x(x-1)(x+2)
=[(Ax-A)(x+2)+Bx^2+2Bx+Cx^2-Cx]/x(x-1)(x+2)
=(Ax^2+2Ax-Ax-2A+Bx^2+2Bx+Cx^2-Cx)/x(x-1)(x+2)
=[(A+B+C)x^2+(A+2B-C)x-2A]/x(x-1)(x+2)
所以(A+B+C)X^2=2X^2
(A+2B-C)X=2X
-2A=-4+3=-1
所以A+B+C=2
A+2B-C=2
A=1/2解得A=1/2,B=1,C=1/2