Question 141
Let $a, b, c$ be positive real numbers such that
$$
\frac{a}{b+c+1}+\frac{b}{a+c+1}+\frac{c}{a+b+1} \leq 1
$$
Prove that:
$$
\frac{1}{b+c+1}+\frac{1}{a+c+1}+\frac{1}{a+b+1} \geq 1
$$
$$
\frac{a}{b+c+1}+\frac{b}{a+c+1}+\frac{c}{a+b+1} \leq 1
$$
Prove that:
$$
\frac{1}{b+c+1}+\frac{1}{a+c+1}+\frac{1}{a+b+1} \geq 1
$$