To simplify the expression \( x + \frac{6}{3^2} - (2 \times 3) + 5 \), we first need to simplify each component step by step.
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Calculate \( 3^2 \): \[ 3^2 = 9 \]
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Now, we substitute \( 3^2 \) back into the expression, specifically in the fraction: \[ x + \frac{6}{9} - (2 \times 3) + 5 \]
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Simplify \( \frac{6}{9} \): \[ \frac{6}{9} = \frac{2}{3} \]
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Calculate \( (2 \times 3) \): \[ 2 \times 3 = 6 \]
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Now, we can rewrite the expression: \[ x + \frac{2}{3} - 6 + 5 \]
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Combine the constants \( -6 + 5 \): \[ -6 + 5 = -1 \]
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Thus, the expression now looks like: \[ x + \frac{2}{3} - 1 \]
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Finally, we write \( -1 \) as a fraction: \[ -1 = -\frac{3}{3} \]
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Combine \( \frac{2}{3} - \frac{3}{3} \): \[ \frac{2}{3} - \frac{3}{3} = \frac{2 - 3}{3} = \frac{-1}{3} \]
Putting everything together, we have: \[ x - 1 + \frac{2}{3} = x - \frac{3}{3} + \frac{2}{3} = x - \frac{1}{3} \]
Therefore, the simplified expression is: \[ x - \frac{1}{3} \] Since the question asks for a "simplified denominator" and not an overall expression, we would recognize that \( \frac{-1}{3} \) has the denominator of \( 3 \).
However, it seems there might be confusion in original responses, as based on the given options (8, 56, 26, -2), none matches \( 3 \).
If we consider what part of the expression has a denominator, we have:
- The term \( \frac{6}{3^2} \) has a denominator of \( 9 \) simplified to \( 3 \).
In conclusion, if asked about a final denominator related to a part of the expression formed in an earlier operation, we would state that the answer is \( 3 \), which was not provided among the options. Therefore, the given answers do not seem to correlate correctly with any step in the simplification. If rechecking the correctness or non-availability of options, the closest consideration would yield an approach of looking through defined values.
For precision, none of the stated options store a match for the derived denominator.