xx-1/(x-2)(x-3)=A+B/x-2+C/x-3,求A,B,C的值

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xx-1/(x-2)(x-3)=A+B/x-2+C/x-3,求A,B,C的值xx-1/(x-2)(x-3)=A+B/x-2+C/x-3,求A,B,C的值xx-1/(x-2)(x-3)=A+B/x-2+

xx-1/(x-2)(x-3)=A+B/x-2+C/x-3,求A,B,C的值
xx-1/(x-2)(x-3)=A+B/x-2+C/x-3,求A,B,C的值

xx-1/(x-2)(x-3)=A+B/x-2+C/x-3,求A,B,C的值
右边通分
=[A(x-2)(x-3)+B(x-3)+C(x-2)]/(x-2)(x-3)
=[Ax²+(B+C-5A)x-(6A+3B+2C)]/(x-2)(x-3)
=(x²-1)/(x-2)(x-3)
对应项系数相等,得:
A=1
B+C-5A=0
6A+3B+2C=1
解方程组,得:
A=1,B=-15,C=20
不懂追问~

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(x^2-1)/(x-2)(x-3)
=(x^2-5x+6+5x-7)/(x-2)(x-3)
=1+(5x-7)/(x-2)(x-3)
A+B/x-2+C/x-3
=A+[B(x-3)+C(x-2)]/(x-2)(x-3)
=A+[(B+C)x-3B-2C]/(x-2)(x-3)
所以:
A=1, B+C=5, 3B+2C=7
A=1,B=-3,C=8