To solve this, we will first convert all the mixed numbers into improper fractions:

3/4 1 1/15 = 3/4 16/15 = 48/60 16/15 = 768/900
1 1/15 2 1/2 = 16/15 5/2 = 80/30 = 8/3
1 3/8 1 1/15 = 11/8 * 16/15 = 176/120

Now, we can perform the calculations:

768/900 + 8/3 - 176/120
= 256/300 + 80/30 - 44/30
= (256+80-44)/30
= 292/30
= 146/15

Therefore, the result is 146/15 or 9 11/15.