Ответ:

[tex]1 \frac{8}{9} \div (1 \frac{3}{4} - 3 \frac{1}{6} ) = \\ = \frac{17}{9} \div ( \frac{7}{4} - \frac{19}{6} ) = \\ = \frac{17}{9} \div \frac{7 \times 3 - 19 \times 2}{12} = \\ = \frac{17}{9} \times ( - \frac{12}{ 17} ) = \\ = - \frac{4}{3} = - 1 \frac{1}{3} [/tex]