Question 146
Let $a$, $b$, $c$ be positive numbers such that $a + b + c = 16$. Prove that
$$
\frac{ab}{a + b} + \frac{bc}{b + c} + \frac{ca}{c + a} \leq 5 + \frac{13c}{16}.
$$
$$
\frac{ab}{a + b} + \frac{bc}{b + c} + \frac{ca}{c + a} \leq 5 + \frac{13c}{16}.
$$