$(2\frac{5}{9} - 1\frac{20}{21}) : 1\frac{8}{49} + 1\frac{8}{9} : 6 = (1\frac{98}{63} - 1\frac{60}{63}) : \frac{57}{49} + \frac{17}{9} * \frac{1}{6} = (1\frac{98}{63} - 1\frac{60}{63}) : \frac{57}{49} + \frac{17}{9} * \frac{1}{6} = \frac{38}{63} * \frac{49}{57} + \frac{17}{54} = \frac{2}{9} * \frac{7}{3} + \frac{17}{54} = \frac{14}{27} + \frac{17}{54} = \frac{28}{54} + \frac{17}{54} = \frac{45}{54} = \frac{5}{6}$

$(1\frac{17}{18} * 1\frac{13}{14} - 2\frac{5}{8} : 1\frac{19}{20}) : (2\frac{25}{78} - 1\frac{1}{26}) = (\frac{35}{18} * \frac{27}{14} - \frac{21}{8} : \frac{39}{20}) : (2\frac{25}{78} - 1\frac{3}{78}) = (\frac{5}{2} * \frac{3}{2} - \frac{21}{8} * \frac{20}{39}) : 1\frac{11}{39} = (\frac{15}{4} - \frac{7}{2} * \frac{5}{13}) : \frac{50}{39} = (\frac{15}{4} - \frac{35}{26}) * \frac{39}{50} = (\frac{195}{52} - \frac{70}{52}) * \frac{39}{50} = \frac{125}{52} * \frac{39}{50} = \frac{5}{52} * \frac{39}{2} = \frac{195}{104} = 1\frac{91}{104} = 1\frac{7}{8}$