分离常数（-2x^2 - 2x+1)/(x^2 + 1)求这个代数式的最大值 怎么办

=[-2(x^2 + 1) - 2x+3 ] /(x^2 + 1)
= -2 -(2x-3) /(x^2 + 1)
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= -2 - 1 /[ x/2 + 3/4 + (13/4) /(2x-3) ]
= -2 - 1 /[ (2x-3)/4 + 3/2 + (13/4) /(2x-3) ]
由于 (2x-3)/4 + (13/4) /(2x-3) ≥ 2√[ ( (2x-3)/4 )·( (13/4) /(2x-3) ) ]
=2√[ ( 1/4 )·( 13/4) ]
= √13 / 2

(-2x^2-2x+1)/(x^2+1)=[-2(x^2+1)+3-2x]/(x^2+1)=-2+(3-2x)/(x^2+1）
对其求导得；f(x)'=[-2(x^2+1)-2x(3-2x)]/(x^2+1)^2=[2x^2-6x-2]/(x^2+1)^2=[2(x-3/2)^2-13/2]/(x^2+1)
令f(x)'=0,得x1=（根号13）/2+3/2,x2=-(根号13)/...