#1237 · Algebra · Quadratics

Range of a rational expression

If $x$ is real, prove that the expression $\frac{( x + m ) ^{2} - 4 mn}{2 ( x - n )}$ admits of all values except such as lie between $2 n$ and $2 m$ .

~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. 8

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