4\21+(1 3\4-11\12)-5\14+1 2\3=

Найдем значение выражения:

4/21 + (1 3/4 - 11/12) - 5/14 + 1 2/3 = 4/21 + 1 3/4 - 11/12 - 5/14 + 1 2/3 = 4/21 + (1 * 4 + 3)/4 - 11/12 - 5/14 + (1 * 3 + 2)/3 = 4/21 + (4 + 3)/4 - 11/12 - 5/14 + (3 + 2)/3 = 4/21 + 7/4 - 11/12 - 5/14 + 5/3 = 4/21 + 5/3 + 7/4 - 11/12 - 5/14 = (4 * 1 + 5 * 7)/21 + (7 * 21 - 11 * 7 - 5 * 6)/84 = (4 + 35)/21 + (147 - 77 - 30)/84 = 39/21 + 40/84 = 13/7 + 10/21 = (13 * 3 + 10 * 1)/21 = (39 + 10)/21 = 49/21 = 7/3; 

В итоге получили, 4/21 + (1 3/4 - 11/12) - 5/14 + 1 2/3 = 7/3.