If \(x,y\) and \(z\) are positive proper fractions satisfying \(x+y+z=2\), prove that \[ \dfrac x{1-x} \cdot \dfrac y{1-y} \cdot \dfrac z{1-z} \ge 8 . \]

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TopNewestSubstitute \(a=1-x,b=1-y,c=1-z\). Simplify the inequality and you find that it is true by AM-HM inequality. – Svatejas Shivakumar · 7 months ago

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