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To simplify the expression, we follow the order of operations (PEMDAS). First, we perform the division and multiplication from left to right, and then perform addition and subtraction from left to right.
12 - 4 ÷ 4 * 3 + 1
Next, we perform the division:
12 - 1 * 3 + 1
Then, we perform the multiplication:
12 - 3 + 1
Finally, we perform the subtraction and addition:
9