# Inequality

Algebra Level 4

If $$a,b,c\geq 0$$, the maximum value of $$N$$ which satisfies the inequality

$\frac{(a+b)(b+c)(c+a)}{(a+b+c)(ab+bc+ca)}\geq N$

can be expressed in the form $$\frac{\alpha}{\beta}$$, where $$\alpha$$ and $$\beta$$ are coprime, positive integers. Find the value of $$\alpha+\beta$$.

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