Rational Domain 80De45

1. **State the problem:** Find the domain of the rational expression $$\frac{(x + 2)(x + 1)}{(x - 1)(x - 3)}$$. 2. **Recall the rule for domain of rational expressions:** The domain includes all real numbers except those that make the denominator zero, because division by zero is undefined. 3. **Set the denominator equal to zero to find excluded values:** $$ (x - 1)(x - 3) = 0 $$ 4. **Solve each factor:** $$ x - 1 = 0 \implies x = 1 $$ $$ x - 3 = 0 \implies x = 3 $$ 5. **Conclusion:** The domain is all real numbers except $$x = 1$$ and $$x = 3$$. **Final answer:** The domain is all real numbers except $$\boxed{1 \text{ and } 3}$$.