Olympiad Problem 2

Algebra Level 3

1x3(y+z)+1y3(x+z)+1z3(x+y)\frac{1}{x^3(y+z)} + \frac{1}{y^3(x+z)} + \frac{1}{z^3(x+y)}

Let xx, yy and zz be positive reals such that xyz=1xyz = 1. If the minimum value of the expression above can be expressed in the form ab\dfrac{a}{b}, find the value of aba - b.

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