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Given two equal quantities, show they are both x+y+z

Source: Finland 2012, Problem 2

May 5, 2013
algebra unsolvedalgebrasystem of equations

Problem Statement

Let x≠1,y≠1x\ne 1,y\ne 1 and x≠y.x\ne y. Show that if yz−x21−x=zx−y21−y,\frac{yz-x^2}{1-x}=\frac{zx-y^2}{1-y}, then yz−x21−x=zx−y21−y=x+y+z.\frac{yz-x^2}{1-x}=\frac{zx-y^2}{1-y}=x+y+z.
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