Question 113
Suppose that $a$, $b$, $c$ are positive real numbers and $a + b + c = 3$. Prove that
$$
\frac{a+b}{c+2} + \frac{b+c}{a+2} + \frac{c+a}{b+2} \ge 2
$$
and determine when equality holds.
$$
\frac{a+b}{c+2} + \frac{b+c}{a+2} + \frac{c+a}{b+2} \ge 2
$$
and determine when equality holds.