Для решения уравнения необходимо найти общий знаменатель и преобразовать выражения:

1) (3/4)/(3/8x - 3/4) - 1/6 = 1/2

(3/4)/(3/8x - 3/4) - 1/6 = 1/2
(3/4)/[(3/8)x - 3/4] - 1/6 = 1/2
(3/4)/[(3/8)x - 3/4] = 1/2 + 1/6
(3/4)/[(3/8)x - 3/4] = 4/12 + 2/12
(3/4)/[(3/8)x - 3/4] = 6/12
(3/4)/[(3/8)x - 3/4] = 1/2
3/(3x - 6) = 4
3 = 4(3x - 6)
3 = 12x - 24
12x = 27
x = 27/12
x = 9/4

2) (2/3)/(1/2x + 1/3) - 1/6 = 1/30

(2/3)/(1/2x + 1/3) - 1/6 = 1/30
(2/3)/[(1/2)x + 1/3] - 1/6 = 1/30
(2/3)/[(1/2)x + 1/3] = 1/30 + 1/6
(2/3)/[(1/2)x + 1/3] = 1/30 + 5/30
(2/3)/[(1/2)x + 1/3] = 6/30
(2/3)/[(1/2)x + 1/3] = 1/5
2/(3x + 2) = 1/5
2 = 3x + 2(5)
2 = 3x + 10
3x = -8
x = -8/3

3) (7/15)/(5/6 - 1/4x - 3/5) = 1/2

(7/15)/(5/6 - 1/4x - 3/5) = 1/2
(7/15)/[5/6 - 1/4x - 3/5] = 1/2
(7/15)/[5/6 - 1/4x - 3/5] = 1/2
(7/15)/[5x/6 - 3/5] = 1/2
(7/15)[(6/5)/(5x/6 - 3/5)] = 1/2
(7/15)(6/5)[1/(5x/6 - 3/5)] = 1/2
(7/15)(6/5)/(5x/6 - 3/5) = 1/2
(42/75)/(5x/6 - 3/5) = 1/2
14/25 = 1/2(5x/6 - 3/5)
14/25 = 5x/12 - 3/10
(14/25)(10) = 10(5x/12 - 3/10)
(14/2) = 5x/6 - 3
7 = 5x/6 - 3
5x/6 = 10
5x = 60
x = 12

Таким образом, решения уравнений:
1) x = 9/4
2) x = -8/3
3) x = 12