Bounds of a symmetric fraction

Shew that $\frac{x ^{2} - x + 1}{x ^{2} + x + 1}$ lies between $3$ and $\frac{1}{3}$ for all real values of $x$ .

~12 minProof · checked by AIrational functionsdiscriminantreal roots

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 3

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