Question

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

Answer 1

(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