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To simplify the denominator of the expression \( 4 + (-6) \cdot 2 / -(-3)^2 \), we first focus on the expression within the denominator, which is:
\[
-(-3)^2
\]
First, we calculate \( (-3)^2 \):
\[
(-3)^2 = 9
\]
Next, we apply the negative sign in front of it:
\[
-(-3)^2 = -9
\]
Thus, the denominator simplifies to \(-9\).
Therefore, the simplified denominator is \(-9\).