1. **State the problem:** Find the excluded values for the rational expression $$\frac{2x^2 + 2x - 3}{x^2 + 12x + 20}$$. 2. **Important rule:** Excluded values are values of $x$ that make the denominator zero because division by zero is undefined. 3. **Set the denominator equal to zero:** $$x^2 + 12x + 20 = 0$$ 4. **Factor the quadratic denominator:** $$x^2 + 12x + 20 = (x + 10)(x + 2)$$ 5. **Find the roots by setting each factor to zero:** $$x + 10 = 0 \implies x = -10$$ $$x + 2 = 0 \implies x = -2$$ 6. **Conclusion:** The excluded values are $x \neq -10, -2$. These values make the denominator zero and are not allowed in the domain of the rational expression.