1. **State the problem:** Simplify the rational expression $$\frac{2u^2 - 8}{u^2 - u - 6}$$. 2. **Factor numerator and denominator:** - Numerator: $$2u^2 - 8 = 2(u^2 - 4) = 2(u - 2)(u + 2)$$ (difference of squares). - Denominator: $$u^2 - u - 6$$ factors as $$(u - 3)(u + 2)$$ because $-3 \times 2 = -6$ and $-3 + 2 = -1$. 3. **Rewrite the expression with factors:** $$\frac{2(u - 2)(u + 2)}{(u - 3)(u + 2)}$$ 4. **Cancel common factors:** The factor $$(u + 2)$$ appears in numerator and denominator, so cancel it: $$\frac{2(u - 2)\cancel{(u + 2)}}{(u - 3)\cancel{(u + 2)}} = \frac{2(u - 2)}{u - 3}$$ 5. **Final simplified form:** $$\boxed{\frac{2(u - 2)}{u - 3}}$$ **Note:** The expression is undefined at $u = -2$ and $u = 3$ because these values make the original denominator zero.