Question 93
Prove that for all $a, b, c \gt 0$ such that $a + b + c \le 3$ the following inequality holds
$$
\frac{a+1}{a(a+2)} + \frac{b+1}{b(b+2)} + \frac{c+1}{c(c+2)} \ge 2.
$$
(Tangenta magazine, 2010)
$$
\frac{a+1}{a(a+2)} + \frac{b+1}{b(b+2)} + \frac{c+1}{c(c+2)} \ge 2.
$$
(Tangenta magazine, 2010)