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To simplify the expression 12 - (4 ÷ 4/3) + 1, we need to follow the order of operations (PEMDAS/BODMAS).
First, we need to solve the division: 4 ÷ 4/3.
To divide by a fraction, we take the reciprocal of the fraction and then multiply. Therefore, 4 ÷ 4/3 is equivalent to 4 × 3/4.
We can cancel out the 4s, leaving us with 3.
Now the expression is simplified to: 12 - 3 + 1.
Next, we can perform the subtraction and addition: 12 - 3 + 1 = 9 + 1 = 10.
Therefore, the simplified form of 12 - 4 ÷ 4/3 + 1 is 10.