NMC 2020 Problem 4

Find all functions $f : R- \{-1\} \to R$ such that $$f(x)f \left( f \left(\frac{1 - y}{1 + y} \right)\right) = f\left(\frac{x + y}{xy + 1}\right)$$ for all $x, y \in R$ that satisfy $(x + 1)(y + 1)(xy + 1) \ne 0$ .