To simplify the given expression \( x + \frac{6}{3^2} - (2 \cdot 3) + 5 \), we first evaluate the denominator \( 3^2 \).
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Calculate \( 3^2 \): \[ 3^2 = 9 \]
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Thus, the expression can be rewritten as: \[ x + \frac{6}{9} - (2 \cdot 3) + 5 \]
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Now calculate \( 2 \cdot 3 \): \[ 2 \cdot 3 = 6 \]
The entire expression becomes: \[ x + \frac{6}{9} - 6 + 5 \]
Now, simplify \( \frac{6}{9} \): \[ \frac{6}{9} = \frac{2}{3} \]
Hence, the expression now is: \[ x + \frac{2}{3} - 6 + 5 \]
The simplified denominator referred to in your question is \( 9 \) as \( 3^2 = 9 \).
Therefore, the simplified denominator is: \[ \boxed{9} \]