stuck in this inequality

Question

$n\in N_+,n\geq 2,x_i>-1,\sum_{i=1}^nx_i=n$ prove that $$\sum_{i=1}^n\frac{1}{1+x_i}\geq\sum_{i=1}^n\frac{x_i}{1+x_i^2}.$$

Answer 1

Hint: $$f(x)=\frac1{1+x}-\frac{x}{1+x^2}+\frac{x-1}4\geqslant0$$

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