1. **State the problem:** Simplify the expression $$\frac{3x - 2}{x^2 - 2x} - \frac{2}{x - 2}$$. 2. **Factor the denominators:** - The first denominator is $$x^2 - 2x = x(x - 2)$$. - The second denominator is already factored as $$x - 2$$. 3. **Rewrite the expression with factored denominators:** $$\frac{3x - 2}{x(x - 2)} - \frac{2}{x - 2}$$. 4. **Find a common denominator:** The common denominator is $$x(x - 2)$$. 5. **Rewrite the second fraction with the common denominator:** $$\frac{2}{x - 2} = \frac{2 \cdot x}{(x - 2) \cdot x} = \frac{2x}{x(x - 2)}$$. 6. **Combine the fractions:** $$\frac{3x - 2}{x(x - 2)} - \frac{2x}{x(x - 2)} = \frac{3x - 2 - 2x}{x(x - 2)}$$. 7. **Simplify the numerator:** $$3x - 2 - 2x = (3x - 2x) - 2 = x - 2$$. 8. **Substitute back:** $$\frac{x - 2}{x(x - 2)}$$. 9. **Cancel the common factor $$x - 2$$ in numerator and denominator:** $$\frac{\cancel{x - 2}}{x \cancel{(x - 2)}} = \frac{1}{x}$$. **Final answer:** $$\boxed{\frac{1}{x}}$$.