#1243 · Algebra · Quadratics

Range of a Rational Expression

Shew that the expression $\frac{( a x - b ) ( d x - c )}{( b x - a ) ( c x - d )}$ will be capable of all values when $x$ is real, if $a^{2} - b^{2}$ and $c^{2} - d^{2}$ have the same sign.

~20 minProof · checked by AIquadratic equationsreal roots conditionrational functions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 14

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