3 1/8 : ( х - 4 7/24) = 17/18 + 1 5/6

Решим уравнение:

3 1/8 : (х - 4 7/24) = 17/18 + 1 5/6;

17/18 + 1 5/6 = 17/18 + (6 + 5)/6 = 17/18 + 11/6 = 17/18 + (3 * 11)/18 = 17/18 + 33/18 = (17 + 33)/18 = 50/18 = 2 14/18 = 2 7/9;

3 1/8 : (х - 4 7/24) = 2 7/9;

3 1/8 = 2 7/9 * (х - 4 7/24);

х - 4 7/24 ≠ 0;

х - 4 7/24 = 3 1/8 : 2 7/9;

х ≠ 4 7/24;

3 1/8 : 2 7/9 = 25/8 : 25/9 = 25/8 * 9/25 = 9/8 = 1 1/8;

х - 4 7/24 = 1 1/8;

х = 1 1/8 + 4 7/24;

1 1/8 + 4 7/24 = 1 + 4 + 1/8 + 7/24 = 5 + (1 * 3)/24 + 7/24 = 5 + 3/24 + 7/24 = 5 + 10/24 = 5 + 5/12 = 5 5/12.

х = 5 5/12;

Ответ: х = 5 5/12.