Вычислите: \(\left(1\frac{1}{9}-5\frac{1}{3}\right):\left(-\frac{1}{5}+2{,}1\right)\).

\[1\frac{1}{9}=\frac{10}{9},\qquad 5\frac{1}{3}=\frac{16}{3}=\frac{48}{9}.\]

\[\left(\frac{10}{9}-\frac{48}{9}\right):\left(-\frac{1}{5}+2.1\right)=\left(-\frac{38}{9}\right):\left(-\frac{1}{5}+\frac{21}{10}\right).\]

\[-\frac{1}{5}+\frac{21}{10}=-\frac{2}{10}+\frac{21}{10}=\frac{19}{10}.\]

\[\left(-\frac{38}{9}\right):\frac{19}{10}=-\frac{38}{9}\cdot\frac{10}{19}=-\frac{20}{9}.\]

Ответ: \(-\frac{20}{9}\).