1. **State the problem:** Simplify the expression $$\frac{7}{3} + \frac{2}{5u}$$ where $u$ is a variable. 2. **Formula and rules:** To add fractions, they must have a common denominator. The common denominator is the least common multiple (LCM) of the denominators. 3. **Find the common denominator:** The denominators are 3 and $5u$. The LCM is $$15u$$. 4. **Rewrite each fraction with the common denominator:** $$\frac{7}{3} = \frac{7 \times 5u}{3 \times 5u} = \frac{35u}{15u}$$ $$\frac{2}{5u} = \frac{2 \times 3}{5u \times 3} = \frac{6}{15u}$$ 5. **Add the fractions:** $$\frac{35u}{15u} + \frac{6}{15u} = \frac{35u + 6}{15u}$$ 6. **Final answer:** $$\boxed{\frac{35u + 6}{15u}}$$ This is the simplified form of the sum of the two fractions.