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# Long inequality

If a,b,c are positive real numbers, prove that :

$\frac{\sqrt{a + b + c} + \sqrt{a}}{b + c} + \frac{\sqrt{a + b + c} + \sqrt{b}}{c + a} + \frac{\sqrt{a + b + c} + \sqrt{c}}{a + b} \ge \frac{9 + 3\sqrt{3}}{2\sqrt{a + b + c}}$

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