已知3x-4/(x-2)(x-1)=a/x-1+b/x-2(a,b为常数）,求a,b的值?

Question

已知3x-4/(x-2)(x-1)=a/x-1 +b/x-2 (a,b为常数）,求a,b 的值?

Answer 1

(3x-4)/(x-2)(x-1)=a/x-1 +b/x-2
(3x-4)/(x-2)(x-1)=[a(x-2)+b(x-1)]/(x-1)(x-2)
(3x-4)/(x-2)(x-1)=[(a+b)x-(2a+b)]/(x-1)(x-2)
a+b=3
2a+b=4
a=1
b=2