# Don't be more, be less!

Algebra Level 4

Let $$x, y, z, t$$ be positive real numbers such that $$\dfrac { 1 }{ 1+x } +\dfrac { 1 }{ 1+y } +\dfrac { 1 }{ 1+z } +\dfrac { 1 }{ 1+t } \ge 3$$.

If the maximum value of $$xyzt$$ can be expressed as $$\frac pq$$, where $$p$$ and $$q$$ are coprime positive integers, then find $$p + q$$.

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