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Question Number 7135 by Master Moon last updated on 12/Aug/16

Prove that

\frac{3}{\sqrt[5]{2} + \sqrt[5]{3} + \sqrt[5]{5}} > \frac{\sqrt[4]{2} + \sqrt[4]{3} + \sqrt[4]{5}}{(\sqrt{2} + \sqrt{3} + \sqrt{5}) (\sqrt[3]{2} + \sqrt[3]{3} + \sqrt[3]{5})}

H o w t o p r o v e i t ?