y=[(x+5)(x+2)]/(x+1)
=(x²+7x+10)/(x+1)
=(x²+7x+6+4)/(x+1)
=(x+1)(x+6)/(x+1)+4/(x+1)
=x+6+4/(x+1)
=(x+1)+4/(x+1)+5
≥2√[(x+1)×4/(x+1)]+5=4+5=9
當(dāng)x+1=4/(x+1)時取等號
解得x=1,另外一個x=-3不符合題意
所以值域y≥9