# Inequality Problem

Algebra Level 4

$\dfrac{ a^3}{(1+b)(1-c)} + \dfrac{b^3}{(1+c)(1-d)} + \dfrac{c^3}{(1+d)(1-a)} +\dfrac{d^3}{(1+a)(1-b)}$

Find minimum value of above expression if $$a,b,c$$ and $$d$$ are positive real numbers such that $$a+b+c+d=1$$.

The minimum value can be expressed as $$\dfrac{ x}{y}$$, where $$x$$ and $$y$$ are relatively prime positive integers. Enter your answer as $$x + y$$.

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