To solve this arithmetic expression, we need to find a common denominator for the fractions involved. In this case, the common denominator is 9.
Converting the fractions:
4/3 = 4/3 * 3/3 = 12/9
4/9 stays the same
5/9 stays the same
Now we can perform the subtraction and addition:
12/9 - 4/9 + 5/9 = (12 - 4 + 5)/9 = 13/9
Therefore, the solution is 13/9