Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
During AMC testing, the AoPS Wiki is in read-only mode and no edits can be made.

1985 OIM Problems/Problem 4

Revision as of 11:36, 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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1985_OIM_Problems/Problem_4&oldid=206968"