答:x>-3,x+3>0
x+1/(x+3)
=(x+3)+1/(x+3)-3
>=2√[(x+3)*1/(x+3)]-3
=2-3
=-1
当且仅当x+3=1/(x+3)即x+3=1、x=-2时取得最小值-1
此题利用了基本不等式a+b>=2√(ab)
答:x>-3,x+3>0
x+1/(x+3)
=(x+3)+1/(x+3)-3
>=2√[(x+3)*1/(x+3)]-3
=2-3
=-1
当且仅当x+3=1/(x+3)即x+3=1、x=-2时取得最小值-1
此题利用了基本不等式a+b>=2√(ab)