Excluded values of a rational expression

Show that if $x$ is real, the expression $(x^{2} - b c) (2 x - b - c)^{- 1}$ has no real values between $b$ and $c$ .

~15 minProof · checked by AIRange of rational functionsDiscriminant method

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 12

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