An algebra problem by Paola Ramírez

Algebra Level pending

Let \(a\), \(b\), and \(c\) be positive real numbers such that \(a+b+c=1\) and always satify the following inequality.

\[\left(\frac{1}{a}-1\right)+\left(\frac{1}{b}-1\right)+\left(\frac{1}{c}-1\right)\geq n\]

Find the maximum value of \(n\).

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