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1985 OIM Problems/Problem 4

Revision as of 12:36, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == If <math>x \ne 1</math>, <math>y \ne 1</math>, <math>x \ne y</math>, and: <cmath>\frac{yz-x^2}{1-x}=\frac{xz-y^2}{1-y}</cmath> Prove that both fractions are equ...")
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Problem

If $x \ne 1$, $y \ne 1$, $x \ne y$, and: \[\frac{yz-x^2}{1-x}=\frac{xz-y^2}{1-y}\] Prove that both fractions are equal to $x+y+z$.

Solution

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