1. **State the problem:** Simplify the expression $$\frac{3x}{15} + \frac{4x}{5}$$. 2. **Find a common denominator:** The denominators are 15 and 5. The least common denominator (LCD) is 15. 3. **Rewrite each fraction with the LCD:** $$\frac{3x}{15} + \frac{4x}{5} = \frac{3x}{15} + \frac{4x \times 3}{5 \times 3} = \frac{3x}{15} + \frac{12x}{15}$$ 4. **Add the fractions:** $$\frac{3x}{15} + \frac{12x}{15} = \frac{3x + 12x}{15} = \frac{15x}{15}$$ 5. **Simplify the fraction:** $$\frac{\cancel{15}x}{\cancel{15}} = x$$ **Final answer:** $$x$$