1. **State the problem:** Simplify the expression $$\frac{3x^2 - 27x}{2x - 9}$$. 2. **Identify the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel common factors. 3. **Factor the numerator:** $$3x^2 - 27x = 3x(x - 9)$$. 4. **Factor the denominator:** $$2x - 9$$ cannot be factored further. 5. **Rewrite the expression:** $$\frac{3x(x - 9)}{2x - 9}$$. 6. **Check for common factors:** The numerator and denominator do not share common factors, so the expression is already simplified. **Final answer:** $$\frac{3x(x - 9)}{2x - 9}$$