MEMO 2016 I1

Let $n \ge 2$ be an integer, and let $x_1, x_2, \ldots, x_n$ be reals for which:

(a) $x_j > -1$ for $j = 1, 2, \ldots, n$ and

(b) $x_1 + x_2 + \ldots + x_n = n.$ Prove that $$\sum_{j = 1}^{n} \frac{1}{1 + x_j} \ge \sum_{j = 1}^{n} \frac{x_j}{1 + x_j^2}$$ and determine when does the equality occur.