To simplify the expression \( 12 - 4 \div 43 + 1 \), we need to follow the order of operations (PEMDAS/BODMAS).
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Division: Calculate \( 4 \div 43 \). \[ 4 \div 43 \approx 0.093 \]
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Subtraction and Addition: Now we can substitute this value back into the expression: \[ 12 - 0.093 + 1 \]
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Calculate \( 12 - 0.093 \): \[ 12 - 0.093 = 11.907 \]
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Now add 1: \[ 11.907 + 1 = 12.907 \]
Thus, the simplified expression is: \[ \boxed{12.907} \]