MathNet 2018-part-03 — 181 problems (EN–VI) Question 107

Let $a\gt 0$ and $x, y \in \mathbb{R}$ be such that $|x|\lt \frac{1}{a}$ and $|y|\lt \frac{1}{a}$. Show that $\left|\frac{x+y}{1+a^{2} x y}\right|\lt \frac{1}{a}$.