Question 142
Let $\mathbb{R}$ denote the set of real numbers. Given a real number $t \neq -1$, find all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
(t + 1)f(1 + xy) - f(x + y) = f(x + 1)f(y + 1)
$$
holds.
$$
(t + 1)f(1 + xy) - f(x + y) = f(x + 1)f(y + 1)
$$
holds.