Решите уравнение
1) 1/3x+1/5x+1/6x=21/40
2) 1/4x+1/6x+1/8x=39/56

1)

1/3х + 1/5х + 1/6х = 21/40

1*10/3*10х + 1*6/5*6х + 1*5/6*5х = 21/40

10/30х + 6/30х + 5/30х = 21/40

21/30х = 21/40

х = 21/40 : 21/30

х = 21/40 * 30/21

х = 21*30/40*21

х = 30/40

х = 3/4

проверка:

1/3 * 3/4 + 1/5 * 3/4 + 1/6 * 3/4 = 21/40

3/12 + 3/20 + 3/24 = 21/40

3*10/12*10 + 3*6/20*6 + 3*5/24*5 = 21/40

30/120 + 18/120 + 15/120 = 21/40

63/120 = 21/40

21/40 = 21/40

2)

1/4х + 1/6х + 1/8х = 39/56

1*6/4*6х + 1*4/6*4х + 1*3/8*3х = 39/56

6/24х + 4/24х + 3/24х = 39/56

13/24х = 39/56

х = 39/56 : 13/24

х = 39/56 * 24/13

х = 39*24/56*13

х = 3*24/56

х = 72/56

х = 72:2/56:2

х = 36/28

х = 36:4/28:4

х = 9/7 или 1 2/7

проверка:

1/4 * 9/7 + 1/6 * 9/7 + 1/8 * 9/7 = 39/56

9/28 + 9/42 + 9/56 = 39/56

9*6/28*6 + 9*4/42*4 + 9*3/56*3 = 39/56

54/168 + 36/168 + 27/168 = 39/56

117/168 = 39/56

39/56 = 39/56

Пошаговое объяснение:

1) 1/3x+1/5x+1/6x=21/40

x(1/3+1/5+1/6)=21/40

x×7/10=21/40

x=(21/40)/(7/10)

x=3/4