MathNet 2023-part-04 — 191 problems (EN–VI) Question 191

Let $a$ be a positive real number. Show that there are no real numbers $b$ and $c$, with $b \lt c$, such that $\left|\frac{x+y}{x-y}\right| \le a$, for every $x, y \in (b, c)$, $x \ne y$.