9. Сократите дробь: \(\dfrac{\sqrt{2}+2\sqrt{50}}{\sqrt{50}+\sqrt{2}}\).

Упростим радикалы: \(\sqrt{50}=5\sqrt{2}\).

Тогда \(\dfrac{\sqrt{2}+2\sqrt{50}}{\sqrt{50}+\sqrt{2}}=\dfrac{\sqrt{2}+10\sqrt{2}}{5\sqrt{2}+\sqrt{2}}=\dfrac{11\sqrt{2}}{6\sqrt{2}}=\dfrac{11}{6}\).

Ответ: \(\dfrac{11}{6}\).