(x+3)/(x+1)=1+2/(x+1)
令1/a=2/(x+1)
则a趋于无穷
x=2a-1
原式=lim(1+1/a)^(2a-1)
=lim[(1+1/a)^a]²÷(1+1/a)
=e²÷1
=e²