Add Rational Expressions 50E6F3

1. **State the problem:** We need to add the rational expressions $$\frac{2x + 1}{x + 3} + \frac{x + 2}{x + 3}$$. 2. **Formula and rule:** When adding rational expressions with the same denominator, we add the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$$ 3. **Apply the rule:** Since both fractions have the denominator $$x + 3$$, add the numerators: $$\frac{2x + 1}{x + 3} + \frac{x + 2}{x + 3} = \frac{(2x + 1) + (x + 2)}{x + 3}$$ 4. **Simplify the numerator:** $$ (2x + 1) + (x + 2) = 2x + 1 + x + 2 = (2x + x) + (1 + 2) = 3x + 3 $$ 5. **Rewrite the expression:** $$ \frac{3x + 3}{x + 3} $$ 6. **Factor the numerator:** $$ 3x + 3 = 3(x + 1) $$ 7. **Substitute back:** $$ \frac{3(x + 1)}{x + 3} $$ 8. **Final answer:** The sum of the rational expressions is $$ \frac{3(x + 1)}{x + 3} $$ This is the simplified form since the numerator and denominator share no common factors to cancel.