$$\frac{12 + 2\sqrt{18}}{\sqrt{50} + \sqrt{2}}$$

$$\frac{12 + 2\sqrt{18}}{\sqrt{50} + \sqrt{2}} = \frac{12 + 2\sqrt{9 \cdot 2}}{\sqrt{25 \cdot 2} + \sqrt{2}} = \frac{12 + 2 \cdot 3\sqrt{2}}{5\sqrt{2} + \sqrt{2}} = \frac{12 + 6\sqrt{2}}{6\sqrt{2}} = \frac{6(2 + \sqrt{2})}{6\sqrt{2}} = \frac{2 + \sqrt{2}}{\sqrt{2}} = \frac{(2 + \sqrt{2})\sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{2\sqrt{2} + 2}{2} = \frac{2(\sqrt{2} + 1)}{2} = \sqrt{2} + 1$$

Ответ: $$\sqrt{2} + 1$$