CH-SMO 2023 Problem 5

Let $D$ be the set of real numbers excluding $-1$ . Find all functions $f: D \to D$ such that for all $x,y \in D$ satisfying $x \neq 0$ and $y \neq -x$ , the equality $$(f(f(x))+y)f \left(\frac{y}{x} \right)+f(f(y))=x$$ holds.