Question 184
The positive numbers $a$, $b$, $c$ are such that
$$
\frac{a}{b+c+1} + \frac{b}{a+c+1} + \frac{c}{a+b+1} \le 1.
$$
Prove that:
$$
\frac{1}{b+c+1} + \frac{1}{a+c+1} + \frac{1}{a+b+1} \ge 1.
$$
$$
\frac{a}{b+c+1} + \frac{b}{a+c+1} + \frac{c}{a+b+1} \le 1.
$$
Prove that:
$$
\frac{1}{b+c+1} + \frac{1}{a+c+1} + \frac{1}{a+b+1} \ge 1.
$$