解：y=(2x^2-2x+3)/(x^2-x+1)=2+1/(x^2-x+1)=2+1/[(x-0.25)^2+0.75]因为(x+0.25)^2+0.75≥0.75所以0＜1/[(x-0.25)^2+0.75]≤4/3所以2＜2+1/[(x-0.25)^2+0.75]≤10/3即2＜y≤10/3所以函数的值域为（2，10/3]
