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Greatest and least values of (x^2 - x + 1)/(x^2 + x + 1)

This type of question, asked 2 times: 11 May 2024 S2, 22 Apr 2025 S1. All 2 questions below, oldest first.

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  1. Question 1

    11 May 2024 S2

    143
    For all real x, the minimum value of 1−x+x21+x+x2\frac{1-x+x^2}{1+x+x^2} is

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  2. Question 2

    22 Apr 2025 S1

    110
    If xx is real, then the difference between the greatest and least values of x2−x+1x2+x+1\frac{x^{2}-x+ 1}{x^{2}+x+ 1} is

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