(3x^2+6x+5)/(x^2/2+x+1)
=(6x^2+12x+10)/(x^2+2x+2)
=[6(x^2+2x+2)-2]/(x^2+2x+2)
=6-2/(x^2+2x+2)
=6-2/[(x+1)^2+1]
(x+1)^2≥0 (x+1)^2+1≥1
0