Baltic Way 1992 · Problem 8

Solution: Since $2^{x}$ must be positive, we have $\frac{2x + 4}{4 - x} > 0$ yielding $-2 < x < 4$. Thus it suffices to check the points $-1, 0, 1, 2, 3$. The three solutions are $x = 0, 1, 2$.