Problem

Source: Iran 3rd round 2017 first Algebra exam

Tags: algebra, functional equation



Find all functions $f:\mathbb{R^+}\rightarrow\mathbb{R^+}$ such that $$\frac{x+f(y)}{xf(y)}=f(\frac{1}{y}+f(\frac{1}{x}))$$for all positive real numbers $x$ and $y$.