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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