Question 130
Let $a, b \gt 1$ be positive integers such that the number $a + b$ divides the number $D(a, b) + v(a, b)$. Here $D(a, b)$ and $v(a, b)$ denote the greatest common divisor and the least common multiple of the numbers $a$ and $b$ respectively. Prove that
$$
\frac{D(a,b) + v(a,b)}{a+b} \le \frac{a+b}{4}.
$$
$$
\frac{D(a,b) + v(a,b)}{a+b} \le \frac{a+b}{4}.
$$