This will give you a run for your money

Algebra Level 5

\[\large \frac{3ab+1}{a+b}+\frac{3bc+1}{b+c}+\frac{3ac+1}{a+c}\] If \(a,b\) and \(c\) are non-negative reals satisfy \(ab+bc+ca=1\), find the minimum value of the expression above.

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