Školjka

%V0 Let $f, g$ and $a$ be polynomials with real coefficients, $f$ and $g$ in one variable and $a$ in two variables. Suppose $$f(x) - f(y) = a(x, y)(g(x) - g(y)) \forall x,y \in \mathbb{R}$$ Prove that there exists a polynomial $h$ with $f(x) = h(g(x)) \text{ } \forall x \in \mathbb{R}.$