3 1/8: (х-4 7/24) = 17/18+1 5/6

Решим уравнение по действиям:

1) 17/18 + 1 5/6 = 17/18 + (1 * 6 + 5) / 6 = 17/18 + 11/6 = 17/18 + 33/18 = (17 + 33) / 18 = 50/18 = 25/9;

2) 3 1/8 = (3 * 8 + 1) / 8 = 25/8;

3) х - 4 7/24 = 24 * х/24 - (4 * 24 + 7) / 24 = 24 * х/24 - 103/24 = (24 * х - 103) / 24;

4) 25/8 : (24 * х - 103) / 24 = 25/8 * 24 / (24 * х - 103) = 75 / (24 * х - 103);

5) 75 / (24 * х - 103) = 25/9;

75 = (24 * х - 103) * 25/9;

24 * х - 103 = 75 * 9/25;

24 * х - 103 = 27;

24 * х = 130;

х = 130/24 = 65/12.

Ответ: х = 65/12.