1. **State the problem:** Simplify the expression $$\frac{3x}{5} + \frac{4x+7}{5}$$. 2. **Formula and rules:** 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 denominator 5, add the numerators: $$\frac{3x}{5} + \frac{4x+7}{5} = \frac{3x + (4x + 7)}{5}$$ 4. **Simplify the numerator:** $$3x + 4x + 7 = 7x + 7$$ 5. **Final simplified expression:** $$\frac{7x + 7}{5}$$ 6. **Factor if desired:** $$\frac{7(x + 1)}{5}$$ **Answer:** $$\frac{7(x + 1)}{5}$$