Difference between revisions of "1985 OIM Problems/Problem 4"

(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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Prove that both fractions are equal to <math>x+y+z</math>.
 
Prove that both fractions are equal to <math>x+y+z</math>.
 
   
 
   
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~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
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== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}
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== See also ==
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https://www.oma.org.ar/enunciados/ibe1.htm

Revision as of 12:25, 13 December 2023

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 $x+y+z$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe1.htm