>>944
 後知恵だが....

 f(x) = (xx+5x+3)/(x+1)^2
    = {(x+1)^2 + 3(x+1) -1}/(x+1)^2
    = 1 +3/(x+1) -1/(x+1)^2
    = 1 +3y -y^2  {← y=1/(x+1)}
    = 13/4 - (3/2 -y)^2
    ≦ 13/4,