To solve these addition problems, we need to find a common denominator for each pair of fractions.

1) 19/42 + 6/7:
The least common denominator for 42 and 7 is 42. Therefore, we can rewrite the fractions as:
(19/42) + (6*6/42) = 19/42 + 36/42 = (19 + 36)/42 = 55/42

2) 3/32 + 5/8:
The least common denominator for 32 and 8 is 32. Therefore, we can rewrite the fractions as:
(3/32) + (5*4/32) = 3/32 + 20/32 = (3 + 20)/32 = 23/32

3) 3/8 + 1/56:
The least common denominator for 8 and 56 is 56. Therefore, we can rewrite the fractions as:
(3/8) + (1*7/56) = 3/8 + 7/56 = (21 + 8)/56 = 29/56

Therefore, the results of the addition problems are:
1) 55/42
2) 23/32
3) 29/56