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$\frac{x+y}{z}=\frac{y+z}{x}=\frac{z+x}{y}=\frac{(x+y)+(y+z)+(z+x)}{x+y+z}=2$
AlgMania
Let $x, y, z$ be nonzero real numbers with$$\frac{x + y}{z}=\frac{y + z}{x}=\frac{z + x}{y}.$$Determine the biggest possible Value of$$\frac{(x + y)(y + z)(z + x)}{xyz}.$$
Equation
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