\frac{\sqrt3 + 1}{\sqrt3 - 1} \cdot \frac{\sqrt3 + 1}{\sqrt3 + 1} = \frac{(\sqrt3 + 1)^2}{(\sqrt3)^2 - (1)^2} = \frac{3 + 2\sqrt3 + 1}3 - 1 = \frac{4 + 2\sqrt3}2 = 2 + \sqrt3. - Dyverse