Question 72
Let $a$, $b$ and $c$ be different positive real numbers such that $(a+b-c)(b+c-a)(c+a-b) \neq 0$. Prove that at least one of the numbers
$$
\frac{a+b}{a+b-c}, \quad \frac{b+c}{b+c-a}, \quad \frac{c+a}{c+a-b}
$$
lies in the interval $(1, 2)$, and that at least one of these numbers does not lie in that interval.
$$
\frac{a+b}{a+b-c}, \quad \frac{b+c}{b+c-a}, \quad \frac{c+a}{c+a-b}
$$
lies in the interval $(1, 2)$, and that at least one of these numbers does not lie in that interval.