(3x2++2x+2)/(x2+x+1)
=2+x^2/(x^2+x+1)
=2+1/(1+1/x+1/x^2)
=1+1/[(1/x+1/2)^2+3/4]
≤1+1/(3/4)
=1+4/3
=7/3
7/3