\(\sqrt{\frac{169}{18}}-\sqrt{\frac{121}{16}}=\)

Упростим каждый корень:

\(\sqrt{\frac{169}{18}}=\frac{13}{\sqrt{18}}=\frac{13}{3\sqrt{2}}=\frac{13\sqrt{2}}{6}\), а \(\sqrt{\frac{121}{16}}=\frac{11}{4}\).

Вычитаем:

\(\frac{13\sqrt{2}}{6}-\frac{11}{4}=\frac{26\sqrt{2}-33}{12}\).

Ответ: \(\frac{26\sqrt{2}-33}{12}\).