已知3x-9 A B C
问题描述：
已知3x-9 A B C
___________ = ____ + ____ + ___
(x²-1)(x-2) x-1 x+1 x-2
求ABC的值
-
答
右边=[A(x+1)(x-2)+B(x-1)(x-2)+B(x-1)(x+1)]/(x-1)(x+1)(x-2)
=[(A+B+C)x²+(-A-3B)x+(-2A+2B-C)]/(x²-1)(x-2)
=(3x-9)/(x²-1)(x-2)
所以(A+B+C)x²+(-A-3B)x+(-2A+2B-C)=3x-9
对应项系数相等
所以A+B+C=0
-A-3B=3
-2A+2B-C=-9
所以A=3,B=-2,C=-1