已知(2x+5)/(x2-1)=A/(x-1)+B/(x+1),求A B的值

已知(2x+5)/(x2-1)=A/(x-1)+B/(x+1),求A B的值
已知(2x+5)/(x2-1)=A/(x-1)+B/(x+1),求A B的值

已知(2x+5)/(x2-1)=A/(x-1)+B/(x+1),求A B的值
(2x+5)/(x2-1)=A/(x-1)+B/(x+1),
=A(x+1)/[(x-1)(x+1)]+B(x-1)/[(x+1)(x-1)]
=[(A-B)+(A+B)x]/(x²-1)
对应相等得
A-B=5
A+B=2
相加得
2A=7 A=7/2
相减得
2B=-3 B=-3/2

(2x+5)/(x²-1)=A/(x-1)+B/(x+1)
(2x+5)/(x²-1)=[A(x+1)+B(x-1)]/(x²-1)
(2x+5)/(x²-1)=[(A+B)x+(A-B)]/(x²-1)
A+B=2
A-B=5
A=7/2,b=-3/2