2/3:5/6x-1/6+1/3=7/9 решить уравнение

Решим уравнение:

2/3 : 5/6 х - 1/6 + 1/3 = 7/9;

2/3 : 5/6 х = 7/9 + 1/6 - 1/3;

7/9 - 1/3 = 7/9 - (1 * 3) / (3 * 3) = 7/9 - 3/9 = (7 - 3) / 9 = 4/9;

4/9 + 1/6 = (4 * 2) / (9 * 2) + (1 * 3) / (6 * 3) = 8/18 + 3/18 = (8 + 3) / 18 = 11/18.

2/3 : 5/6 х = 11/18.

Умножим уравнение на 5/6 х:

2/3 = 11/18 * 5/6 х;

5/6 х ≠ 0;

х ≠ 0.

11/18 * 5/6 = (11 * 5) / (18 * 6) = 55/108.

2/3 = 55/108 х;

х = 2/3 : 55/108;

х = 2/3 * 108/55;

х = (2 * 108) / (3 * 55);

х = (2 * 3 * 36) / (3 * 55);

х = (2 * 36) / 55;

х = 72/55;

х = 1 17/55.

Ответ: х = 1 17/55.