已知3x+1/x²+2x-3=A/x-1+B/x+3,求A,B的值

已知3x+1/x²+2x-3=A/x-1+B/x+3,求A,B的值
已知3x+1/x²+2x-3=A/x-1+B/x+3,求A,B的值

已知3x+1/x²+2x-3=A/x-1+B/x+3,求A,B的值
答：
(3x+1)/(x²+2x-3)=A/(x-1)+B/(x+3)
(3x+1)/[(x-1)(x+3)]=A(x+3)/[(x-1)(x+3)]+B(x-1)/[(x-1)(x+3)]
A(x+3)+B(x-1)=3x+1
(A+B)x+3A-B=3x+1
A+B=3
3A-B=1
解得：A=1,B=2