5x+1 дробь3=1+8xдробь5

1) (5x + 1) / 3 = (1 + 8x) / 5,

Мы должни сделать перекрестное умножение. Итак:

5 * (5x + 1) = 3 * (1 + 8x),

25x + 5 = 3 + 24x,

25x - 24x = 3 - 5,

x = - 2.

Проверка: (5 * ( - 2) + 1) / 3 = (1 + 8 * ( - 2)) / 5,

(-10 + 1) / 3 = (1 + (-16)) / 5,

-9/3 = (1 - 16) / 5,

- 3 = - 15/5,

- 3 = - 3.

2) 5x+1/3=1+8x/5,

5x - 8x/5 = 1 - 1/3

((5:1) * 5x - 8x) / 5 = ((3:1) * 1 - 1) / 3,

(5 * 5x - 8x) / 5 = (3*1 - 1) / 3,

(25x - 8x) / 5 = (3 - 1) / 3,

17x/5 = 2/3,

17x = 5 * 2/3,

17x = 10/3,

x = 10/3 : 17,

x = 10/3 * 1/17,

x = (10 * 1) / (3 * 17),

x = 10/51,

Проверка: 5 * (10/51) + 1/3=1 + (8 * (10/51)) / 5,

50/51 + 1/3 = 1 + (80/51) / 5,

(50+17) / 51 = 1 + (80/51 * 1/5),

67/51 = 1 + (80*1) / (51 * 5),

67/51 = 1 + (16*1) / 51,

67/51 = (51 + 16) / 51,

67/51 = 67/51.

Ответ: 1) x = - 2, 2) x = 10/51.