Вычислите: $$\frac{9}{10} + \frac{4}{9} : \left(2 - \frac{11}{21}\right) - 1\frac{2}{3}$$

$$2 - \frac{11}{21} = \frac{2 \cdot 21}{21} - \frac{11}{21} = \frac{42}{21} - \frac{11}{21} = \frac{42-11}{21} = \frac{31}{21}$$


$$\frac{4}{9} : \frac{31}{21} = \frac{4}{9} \cdot \frac{21}{31} = \frac{4 \cdot 21}{9 \cdot 31} = \frac{4 \cdot 7}{3 \cdot 31} = \frac{28}{93}$$


$$\frac{9}{10} + \frac{28}{93} = \frac{9 \cdot 93}{10 \cdot 93} + \frac{28 \cdot 10}{93 \cdot 10} = \frac{837}{930} + \frac{280}{930} = \frac{837 + 280}{930} = \frac{1117}{930}$$


$$1\frac{2}{3} = \frac{1 \cdot 3 + 2}{3} = \frac{5}{3}$$


$$\frac{1117}{930} - \frac{5}{3} = \frac{1117}{930} - \frac{5 \cdot 310}{3 \cdot 310} = \frac{1117}{930} - \frac{1550}{930} = \frac{1117 - 1550}{930} = \frac{-433}{930}$$