求分式方程中A,B,C三数的值

题目

求分式方程中A,B,C三数的值
x^2-x-3 A B C
_______________ = ____ +____ + ____ ,求A,B,C的值.
(x-1)(x-2)(x-3) x-1 x-2 x-3
请给出完整的过程,

答案

[x^2-x-3]/ (x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-3)
去分母得:
x^2-x-3=A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2)
令x=1得:
1-1-3=A(1-2)(1-3),得A=-3/2
令x=2得:
4-2-3=B(2-1)(2-3),得B=1
令x=3得:
9-3-3=C(3-1)(3-2),得C=3/2