$(\frac{5}{6} - \frac{3}{8}) : \frac{3}{4} - (\frac{3}{8} + \frac{7}{20}) : 1\frac{9}{20} = \frac{5 * 8 - 3 * 6}{48} : \frac{3}{4} - \frac{3 * 5 + 7 * 2}{40} : 1\frac{9}{20} = \frac{40 - 18}{48} * \frac{4}{3} - \frac{15 + 14}{40} : \frac{29}{20} = \frac{22}{48} * \frac{4}{3} - \frac{29}{40} * \frac{20}{29} = \frac{22}{4 * 12} * \frac{4}{3} - \frac{29}{40} * \frac{20}{29} = \frac{22}{36} - \frac{20}{40} = \frac{11}{18} - \frac{1}{2} = \frac{11 - 9}{18} = \frac{2}{18} = \frac{1}{9}$