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Maximum value of \( f(x)=\frac{x^{2}-x+1}{x^{2}+x+1} \).

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Maximum value of \( f(x)=\frac{x^{2}-x+1}{x^{2}+x+1} \).

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⇒ x = −1, f(x) = 3   (maxima)

Hence, the answer is 3.

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