Question

若等式(5x-4)/(x-2)(x-5)=A/(x-2)+B/(x-5)恒成立,求A,B的值

Answer 1

A/(x-2)+B/(x-5)=[A(x-5)+B(x-2)]/(x-2)(x-5) =[(A+B)X+(-5A-2B)]/(x-2)(x-5)

与左边等式对比得：

A＋B＝5,－5A－2B＝－4

联立两式解方程组得：

A=-2,B=7