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.