f(x)=(x^2-2x+6)/(x+1)
=[x^2+2x+1-4x+5]/(x+1)
=[(x+1)^2-4(x+1)+9]/(x+1)
=(x+1) + 9/(x+1) - 4
因为x>-1
所以x+1>0
所以(x+1) + 9/(x+1) - 4>=2根号9 - 4=6-4=2