\[\large \frac{3ab+1}{a+b}+\frac{3bc+1}{b+c}+\frac{3ac+1}{a+c} \geq Kabc\]

If \(a,b\) and \(c\) are positive real numbers satisfying \(ab+bc+ca=1\), find the maximum \(K\) for which the inequality holds.

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