1. **State the problem:** Simplify the expression $$\frac{2}{3x} + \frac{1}{7x}$$ and leave the answer in its simplest form. 2. **Identify the common denominator:** Both terms have $x$ in the denominator, so the common denominator is $$3x \times 7 = 21x$$. 3. **Rewrite each fraction with the common denominator:** $$\frac{2}{3x} = \frac{2 \times 7}{3x \times 7} = \frac{14}{21x}$$ $$\frac{1}{7x} = \frac{1 \times 3}{7x \times 3} = \frac{3}{21x}$$ 4. **Add the fractions:** $$\frac{14}{21x} + \frac{3}{21x} = \frac{14 + 3}{21x} = \frac{17}{21x}$$ 5. **Simplify the fraction:** The numerator 17 and denominator 21 have no common factors other than 1, so the fraction is already in simplest form. **Final answer:** $$\frac{17}{21x}$$