First, we will convert all mixed numbers to improper fractions:

12 5/12 = 12 + 5/12 = 144/12 + 5/12 = 149/12
1 2/3 = 1 + 2/3 = 3/3 + 2/3 = 5/3
3 5/6 = 3 + 5/6 = 18/6 + 5/6 = 23/6
2 3/4 = 2 + 3/4 = 8/4 + 3/4 = 11/4
2 1/2 = 2 + 1/2 = 4/2 + 1/2 = 5/2

Now, let's simplify the expression:

((149/12) + (5/3) - (23/6) + (11/4)) ÷ ((5/2) (2/5) - (7/9))
((149/12) + 5/3 - 23/6 + 11/4) ÷ (5/2 2/5 - 7/9)
((149/12) + 20/12 - 23/6 + 33/12) ÷ (10/10 - 7/9)
((149 + 20 - 46 + 33) / 12) ÷ (3/10)
(156 / 12) ÷ (3/10)
13 ÷ (3/10)
13 * (10/3)
130/3
43 1/3

Therefore, (12 5/12 + 1 2/3 - 3 5/6 + 2 3/4) ÷ (2 1/2 * 2/5 - 7/9) simplifies to 43 1/3.