Question 5
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that satisfy the conditions
$$
f(1+x y)-f(x+y)=f(x) f(y) \quad \text { for all } x, y \in \mathbb{R}
$$
and $f(-1) \neq 0$.
$$
f(1+x y)-f(x+y)=f(x) f(y) \quad \text { for all } x, y \in \mathbb{R}
$$
and $f(-1) \neq 0$.