To solve this, we first need to simplify the fractions by finding a common denominator.

4/9 = 16/36
5/6 = 30/36
7/18 = 14/36
1/12 = 3/36
1 1/4 = 5/4 = 45/36

Now we can rewrite the expression with a common denominator:

(16/36) + (30/36) + (14/36) - (3/36 + 45/36)

Now we can add and subtract the fractions:
16/36 + 30/36 + 14/36 - 3/36 - 45/36
= (16 + 30 + 14 - 3 - 45) / 36
= 12 / 36
= 1/3

Therefore, 4/9 + 5/6 + 7/18 - (1/12 + 1 1/4) = 1/3