求分式y=3x^2+6x+5/x^2+2x+2的取值范围

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求分式y=3x^2+6x+5/x^2+2x+2的取值范围
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求分式y=3x^2+6x+5/x^2+2x+2的取值范围
求分式y=3x^2+6x+5/x^2+2x+2的取值范围

求分式y=3x^2+6x+5/x^2+2x+2的取值范围
3x^2+6x+5 = 3(x^2+2x+2) -1
所以 y = 3x^2+6x+5/x^2+2x+2 = 3 - 1/(x^2+2x+2)
因为 x^2+2x+2 = (x+1)^2 +1 >=1,
所以 0

y=3x^2+6x+5/x^2+2x+2
=3x^2+6x+6-1/x^2+2x+2
=3+[-1/(x+1)^2+1]
(x+1)^2+1大于等于1
-1+3大于等于3+[-1/(x+1)^2+1]大于0+3
y属于[2,3)