Question 153
Find all functions $f: Q^+ \to Q^+$ such that
$$
f(x) + f(y) + 2xyf(xy) = \frac{f(xy)}{f(x+y)}, \qquad \textcircled{1}
$$
Where $Q^+ = \{q \mid q \text{ is a positive rational number}\}$.
$$
f(x) + f(y) + 2xyf(xy) = \frac{f(xy)}{f(x+y)}, \qquad \textcircled{1}
$$
Where $Q^+ = \{q \mid q \text{ is a positive rational number}\}$.