Try this inequality, guys! I already solved it but I just want different solutions. (Source: KVS JMO 2014 - P8)

If \(a,b,c\) are positive real numbers, prove that: \[ \dfrac{ \sqrt{a+b+c} + \sqrt a}{b+c} + \dfrac{ \sqrt{a+b+c} + \sqrt b}{c+a} + \dfrac{ \sqrt{a+b+c} + \sqrt c}{a+b} \geq \dfrac{9 + 3\sqrt3}{2\sqrt{a+b+c}} \]

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