To solve this expression, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's simplify the multiplication and division within the expression:

2/9 x 3/4 = (2 x 3) / (9 x 4) = 6/36 = 1/6

Now, let's substitute this value back into the expression:

1/3 + 1/6

To add these fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6. So, we can rewrite the fractions with a common denominator:

1/3 + 1/6 = 2/6 + 1/6

Now, we can add the fractions:

2/6 + 1/6 = 3/6

Finally, we can simplify the fraction:

3/6 = 1/2

Therefore, 1/3 + 2/9 x 3/4 = 1/2.