y - y-3
3
___________
4 + 2
9 3
To simplify the given expression (y - (y - 3))/3 ÷ (4 + 2/9 - 3/3), we need to follow the order of operations (PEMDAS/BODMAS).
Step 1: Simplify the numerator (y - (y - 3))/3
We have y - (y - 3) in the numerator. Distributing the negative sign inside parentheses, we get y - y + 3. Combining like terms, y - y simplifies to 0, so the numerator becomes 3.
Step 2: Simplify the denominator (4 + 2/9 - 3/3)
We have 4 + 2/9 - 3/3 in the denominator. We need to find a common denominator to add/subtract these fractions.
To do this, we convert the whole number 4 to a fraction with the common denominator of 9:
4 = 36/9
Now, the expression becomes (36/9 + 2/9 - 3/3). We have a common denominator of 9, so we can add/subtract these fractions now:
36/9 + 2/9 - 3/3 = (36 + 2 - 9)/9 = 29/9
So, the expression becomes 3/((29/9)/3).
Step 3: Simplify the division (3/((29/9)/3))
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of (29/9)/3 is 3/(29/9), so we can rewrite the expression as 3 * (9/29) = (3/1) * (9/29) = 27/29.
Therefore, the simplified expression is 27/29.