1. **State the problem:** Simplify the expression $$\frac{x^2 - 2x}{x^2 + 2x}$$ given that $$x \neq -2$$ and compare it to $$\frac{-2}{x+2}$$. 2. **Recall the formula and rules:** To simplify rational expressions, factor numerator and denominator and cancel common factors, but remember to exclude values that make the denominator zero. 3. **Factor numerator and denominator:** $$x^2 - 2x = x(x - 2)$$ $$x^2 + 2x = x(x + 2)$$ 4. **Rewrite the expression:** $$\frac{x(x - 2)}{x(x + 2)}$$ 5. **Cancel common factors:** $$\frac{\cancel{x}(x - 2)}{\cancel{x}(x + 2)} = \frac{x - 2}{x + 2}$$ 6. **State the simplified form:** The simplified expression is $$\frac{x - 2}{x + 2}$$. 7. **Domain restriction:** Since $$x \neq -2$$ (to avoid division by zero), the simplification is valid for all $$x$$ except $$x = -2$$ and also $$x \neq 0$$ because the original denominator has $$x$$ as a factor. **Final answer:** $$\frac{x - 2}{x + 2}$$