曲线y=4(x+1)²/(x²+2x+4)
=4(x+1)²/[(x+1)²+3]
=4-12/[(x+1)²+3]
可得,当x趋于±∞时,12/[(x+1)²+3]趋于0.
∴y→4.
∴曲线的水平渐近线方程为y=4.