To simplify the expression \((\frac{1}{9} \cdot 9) \cdot x - 9\), we can first simplify \(\frac{1}{9} \cdot 9\).
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Calculate \(\frac{1}{9} \cdot 9\): \[ \frac{1}{9} \cdot 9 = 1 \]
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Now, substitute this back into the expression: \[ (1) \cdot x - 9 = x - 9 \]
Therefore, the expression \((\frac{1}{9} \cdot 9) \cdot x - 9\) simplifies to: \[ x - 9 \]
Thus, the equivalent expression is \(x - 9\).