Unusual Proportions

Algebra Level 3

If for three distinct positive numbers x,yx,y and zz,

yx−z=x+yz=xy, \dfrac y{x-z} = \dfrac{x+y}z = \dfrac xy,

then find the numerical value of xy\dfrac xy.

AHSME 1992.
Mike Argus by Mike Argus
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