Question 130
Let $a$, $b$, $c$ be three non-negative real numbers such that $a + b + c = 3$. Prove the inequality:
$$
\frac{a}{1 + b} + \frac{b}{1 + c} + \frac{c}{1 + a} \ge \frac{1}{1 + a} + \frac{1}{1 + b} + \frac{1}{1 + c}.
$$
$$
\frac{a}{1 + b} + \frac{b}{1 + c} + \frac{c}{1 + a} \ge \frac{1}{1 + a} + \frac{1}{1 + b} + \frac{1}{1 + c}.
$$