已知n²+3n分之1=n分之A + n+3分之B则A=___ B=___

已知n²+3n分之1=n分之A + n+3分之B则A=___ B=___
已知n²+3n分之1=n分之A + n+3分之B则A=___ B=___

已知n²+3n分之1=n分之A + n+3分之B则A=___ B=___
1/(n²+3n)=A/n+B/(n+3)=A(n+3)/(n²+3n)+Bn/(n²+3n)
A(n+3)+Bn
=An+3A+Bn
=(A+B)n+3A=1
A+B=0
3A=1 A=1/3
B=-1/3

A=1/3 B=-1/3

1/n²+3n=A/n+B/n+3=[A(n+3)+Bn]/n(n+3)
A(n+3)+Bn=1
A+B=0
3A=1
A=1/3
B=-1/3

1/(n²+3n)=1/[n(n+3)]=(1/3)[1/n -1/(n+3)]=(1/3)/n +(-1/3)/(n+3)
A=1/3 B=-1/3