Bounds of a rational fraction

If $x$ be real, prove that $\frac{x}{x ^{2} - 5 x + 9}$ must lie between $1$ and $- \frac{1}{11}$ .

~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. 2

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