若2x+1/(x+1)*(x+2)=A/x+1+B/x+2恒成立,则A+B=____

若2x+1/(x+1)*(x+2)=A/x+1+B/x+2恒成立,则A+B=____
若2x+1/(x+1)*(x+2)=A/x+1+B/x+2恒成立,则A+B=____

若2x+1/(x+1)*(x+2)=A/x+1+B/x+2恒成立,则A+B=____
1.通分
所以
2x+1/(x+1)*(x+2)=A(x+2)+B(x+1)/(x+1)*(x+2)
2x+1/(x+1)*(x+2)=Ax+2A+Bx+B/(x+1)*(x+2)
2x+1/(x+1)*(x+2)=(A+B)x+2A+B/(x+1)*(x+2)
所以
A+B=2
2A+B=1
解这个方程组得
A=-1
B=3
所以A+B=2
写了可长时间了``