\[\frac{x^{2} - 6x + 9}{x^{2} - 3x + 9} \cdot \frac{x^{3} + 27}{3x - 9} =\]
\[= \frac{(x - 3)^{2} \cdot (x + 3)\left( x^{2} - 3x + 9 \right)}{\left( x^{2} - 3x + 9 \right) \cdot 3 \cdot (x - 3)} =\]
\[= \frac{(x - 3)(x + 3)}{3} = \frac{x^{2} - 9}{3}\]