To add these fractions, we need to find a common denominator. The least common multiple of 7 and 8 is 56.

To convert 3/7 to have a denominator of 56, we multiply the numerator and denominator by 8: (3/7) * (8/8) = 24/56.

To convert 5/8 to have a denominator of 56, we multiply the numerator and denominator by 7: (5/8) * (7/7) = 35/56.

Now that both fractions have a common denominator of 56, we can add them: 24/56 + 35/56 = 59/56.

Therefore, 3/7 + 5/8 = 59/56.