Find all functions f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}, such that for all $x, y \in \mathbb{R}^{+}$it holds that
f\left(x y\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{x+y}\right)\right)=f\left(x y\left(\frac{1}{x}+\frac{1}{y}\right)\right)+f(x) f\left(\frac{y}{x+y}\right)