Question

若式子(A/x-3)+(B/x+1)=(x+5)/(x-3)×(x+1)成立,求常数A、B的值

Answer 1

若式子(A/x-3)+(B/x+1)=(x+5)/(x-3)×(x+1)成立

(A(x+1)+B(x-3))/(x-3)(x+1)=(x+5)/(x-3)(x+1)

((A+B)x+A-3B)/(x-3)(x+1)=(x+5)/(x-3)(x+1)

A+B=1

A-3B=5

解得

A=2

B=-1