Problem:
Exercise 65. If $a_1, a_2, \ldots, a_n \in \mathbb{R}^+$ and $s = a_1 + a_2 + \cdots + a_n$, then \begin{equation} \frac{a_1}{s-a_1} + \frac{a_2}{s-a_2} + \cdots + \frac{a_n}{s-a_n} \geq \frac{n}{n-1} . \end{equation}
Now, we have to prove this Inequality using the Rearrangement Inequality. I began by considering assuming (WLOG) that $a_1\leq a_2\leq a_3...\leq a_n$. If $m_i=s-a_i$ then ${1\over m_1}\leq{1\over m_2}.....\leq{1\over m_n}$. Thus we can see that the LHS is maximal. But I am unsure about which permutation of $(a_1,a_2,...a_n)$ should I consider in order to get the RHS.