Question

这是《实验班》上的,若x-3/(x+1)(x-1)=A/x+1+B/x-1,求A,B的值.

Answer 1

(x-3)/(x+1)(x-1)=A/(x+1)+B/(x-1)(通分)

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

(x-3)/(x+1)(x-1)=[A(x-1)+B(x+1)]/(x+1)(x-1)

(x-3)/(x+1)(x-1)=(Ax-A+Bx+B)/(x+1)(x-1)

(x-3)/(x+1)(x-1)=[(A+B)x-(A-B)]/(x+1)(x-1)

A+B=1

A-B=3

解得

A=2

B=-1