a) \[\left(\frac{5}{6} + \frac{4}{9}\right) - \frac{5}{6} \cdot \frac{4}{9} = \left(\frac{5 \cdot 3}{6 \cdot 3} + \frac{4 \cdot 2}{9 \cdot 2}\right) - \frac{5 \cdot 4}{6 \cdot 9} = \left(\frac{15}{18} + \frac{8}{18}\right) - \frac{20}{54} = \frac{23}{18} - \frac{20}{54} = \frac{23 \cdot 3}{18 \cdot 3} - \frac{20}{54} = \frac{69}{54} - \frac{20}{54} = \frac{49}{54}\]
Ответ: \(\frac{49}{54}\)