To add 3/14 and 5/7, we need to find a common denominator. The least common denominator between 14 and 7 is 14.

(3/14) + (5/7) = (3/14) + (10/14) = 13/14

So 3/14 + 5/7 = 13/14

To simplify 19/24/(3/16 + 5/24), we first need to find a common denominator for the fractions in the denominator.

3/16 = 9/48
5/24 = 10/48

So, we have:

19/24 / (9/48 + 10/48)

Now, we can add the fractions in the denominator:

19/24 / (9/48 + 10/48) = 19/24 / 19/48

To divide by a fraction, we multiply by its reciprocal:

19/24 * 48/19 = 48/24 = 2

Therefore, 19/24 / (3/16 + 5/24) simplifies to 2.