To add or subtract fractions, we need to have a common denominator. In this case, the common denominator is 105, which is the least common multiple of 35, 24, and 3.

Now, let's convert each fraction to have a denominator of 105:

13/35 = (13/35) * (3/3) = 39/105
8/24 = (8/24) * (4/4) = 32/96
22/35 = (22/35) * (3/3) = 66/105
4/3 = (4/3) * (35/35) = 140/105

Now, we can add or subtract the fractions:

39/105 + 32/96 + 66/105 - 140/105

To add or subtract fractions, we need to have the same denominator. In this case, the denominator is already the same, so we can simply add or subtract the numerators:

(39 + 32 + 66 - 140) / 105

= (-3) / 105

= -1/35

Therefore, 13/35 + 8/24 + 22/35 - 4/3 = -1/35.