(8 1\6-5\18):14\27-(10 7\8 : 3\4*2\3+5 3\7 : 6 1\3)*3\17

Решим пример по действиям:

1) 8 1/6 - 5/18 = (8 * 6 + 1)/6 - 5/18 = 49/6 - 5/18 = 147/18 - 5/18 = (147 - 5)/18 = 142/18 = 71/9;

2) 71/9 : 14/27 = 71/9 * 27/14 = (71 * 27)/(9 * 14) = 213/14;

3) 10 7/8 : 3/4 * 2/3 = (10 * 8 + 7)/8 * 4/3 * 2/3 = 87/8 * 4/3 * 2/3 = (87 * 4 * 2)/(8 * 3 * 3) = 29/3;

4) 5 3/7 : 6 1/3 = (5 * 7 + 3)/7 : (6 * 3 + 1)/3 = 38/7 : 19/3 = 38/7 * 3/19 = (38 * 3)/(7 * 19) = 6/7;

5) 29/3 + 6/7 = 203/21 + 18/21 = 221/21;

6) 221/21 * 3/17 = 13/7;

7) 213/14 - 13/7 = 213/14 - 26/14 = 187/14.

Ответ: 187/14.