* ДОП. \(\frac{3 \frac{1}{8} : \frac{15}{16} - \frac{1}{4}}{(\frac{2}{7} + \frac{5}{21}) : 1 \frac{4}{7}} - \frac{(\frac{8}{12} - 2 \frac{5}{12}) : 2 \frac{1}{6}}{1 \frac{7}{12} : (8 \frac{3}{8} + \frac{5}{12})} - 1 \frac{9}{20}\)

Выполним действия по порядку:

1) \(3 \frac{1}{8} : \frac{15}{16} = \frac{25}{8} : \frac{15}{16} = \frac{25}{8} \cdot \frac{16}{15} = \frac{25 \cdot 16}{8 \cdot 15} = \frac{5 \cdot 2}{1 \cdot 3} = \frac{10}{3}\)

2) \(\frac{10}{3} - \frac{1}{4} = \frac{40}{12} - \frac{3}{12} = \frac{37}{12}\)

3) \(\frac{2}{7} + \frac{5}{21} = \frac{6}{21} + \frac{5}{21} = \frac{11}{21}\)

4) \(1 \frac{4}{7} = \frac{11}{7}\)

5) \(\frac{11}{21} : \frac{11}{7} = \frac{11}{21} \cdot \frac{7}{11} = \frac{1}{3}\)

6) \(\frac{\frac{37}{12}}{\frac{1}{3}} = \frac{37}{12} : \frac{1}{3} = \frac{37}{12} \cdot \frac{3}{1} = \frac{37}{4}\)

7) \(\frac{8}{12} = \frac{2}{3}\)

8) \(2 \frac{5}{12} = \frac{29}{12}\)

9) \(\frac{2}{3} - \frac{29}{12} = \frac{8}{12} - \frac{29}{12} = -\frac{21}{12} = -\frac{7}{4}\)

10) \(2 \frac{1}{6} = \frac{13}{6}\)

11) \(-\frac{7}{4} : \frac{13}{6} = -\frac{7}{4} \cdot \frac{6}{13} = -\frac{7 \cdot 3}{2 \cdot 13} = -\frac{21}{26}\)

12) \(1 \frac{7}{12} = \frac{19}{12}\)

13) \(8 \frac{3}{8} = \frac{67}{8}\)

14) \(\frac{67}{8} + \frac{5}{12} = \frac{201}{24} + \frac{10}{24} = \frac{211}{24}\)

15) \(\frac{19}{12} : \frac{211}{24} = \frac{19}{12} \cdot \frac{24}{211} = \frac{19 \cdot 2}{1 \cdot 211} = \frac{38}{211}\)

16) \(-\frac{\frac{21}{26}}{\frac{38}{211}} = -\frac{21}{26} : \frac{38}{211} = -\frac{21}{26} \cdot \frac{211}{38} = -\frac{21 \cdot 211}{26 \cdot 38} = -\frac{4431}{988}\)

17) \(1 \frac{9}{20} = \frac{29}{20}\)

18) \(\frac{37}{4} - (-\frac{4431}{988}) - \frac{29}{20} = \frac{37}{4} + \frac{4431}{988} - \frac{29}{20} = \frac{9182}{988} + \frac{4431}{988} - \frac{1421}{988} = \frac{12192}{988} = \frac{3048}{247} \approx 12.34\)

Ответ: \(\frac{3048}{247}\)