# Inequality of Numerators

Algebra Level 2

Let $$a,b,c$$ be positive reals. Also, let $$k$$ be the largest possible real such that

$\dfrac{a}{1}+\dfrac{b}{1}+\dfrac{c}{1}+\dfrac{a+b}{1}+\dfrac{b+c}{1}+\dfrac{c+a}{1}\le \dfrac{a+b+c}{k}.$

If $$k$$ can be expressed as $$\frac{p}{q}$$ for relatively prime positive integers $$p$$ and $$q$$, then what is $$p+q?$$

Inequality of Denominators, the harder version of this inequality

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