Question: (2x + 1)/(x + 3) + (x + 2)/(x + 3)
1. **State the problem:** Simplify the expression $$\frac{2x + 1}{x + 3} + \frac{x + 2}{x + 3}$$.
2. **Formula and rule:** When adding fractions with the same denominator, 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 same 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:**
$$ (2x + 1) + (x + 2) = 2x + 1 + x + 2 = 3x + 3 $$.
5. **Rewrite the fraction:**
$$ \frac{3x + 3}{x + 3} $$.
6. **Factor the numerator:**
$$ 3x + 3 = 3(x + 1) $$.
7. **Substitute back:**
$$ \frac{3(x + 1)}{x + 3} $$.
8. **Final expression:** The simplified form is $$\frac{3(x + 1)}{x + 3}$$.
**Note:** The expression cannot be simplified further because $$x + 1$$ and $$x + 3$$ are different factors.
**Answer:** $$\frac{3(x + 1)}{x + 3}$$.