Question 19
Let $a$, $b$ and $c$ be real numbers larger than $1$. Prove the inequality
$$
\frac{ab}{c-1} + \frac{bc}{a-1} + \frac{ca}{b-1} \geq 12.
$$
When does equality hold?
$$
\frac{ab}{c-1} + \frac{bc}{a-1} + \frac{ca}{b-1} \geq 12.
$$
When does equality hold?