Question 69
Find all functions $f: (0, +\infty) \to \mathbb{R}$ satisfying
$$
f(x) - f(x + y) = f\left(\frac{x}{y}\right) f(x + y) \quad \text{for all } x, y \gt 0.
$$
$$
f(x) - f(x + y) = f\left(\frac{x}{y}\right) f(x + y) \quad \text{for all } x, y \gt 0.
$$