Olympiad Problem 2

Algebra Level 3

\[\frac{1}{x^3(y+z)} + \frac{1}{y^3(x+z)} + \frac{1}{z^3(x+y)}\]

Let \(x\), \(y\) and \(z\) be positive reals such that \(xyz =  1\). If the minimum value of the expression above can be expressed in the form \(\dfrac{a}{b}\), find the value of \(a - b\).

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