For positive numbers $a_1,a_2,\ldots,a_n$ ($n\ge2$) denote $s=a_1+\ldots+a_n$. Prove that $$\frac{a_1}{s-a_1}+\ldots+\frac{a_n}{s-a_n}\ge\frac n{n-1}.$$
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Tags: inequalities
For positive numbers $a_1,a_2,\ldots,a_n$ ($n\ge2$) denote $s=a_1+\ldots+a_n$. Prove that $$\frac{a_1}{s-a_1}+\ldots+\frac{a_n}{s-a_n}\ge\frac n{n-1}.$$