Question: User: $\frac{4}{3m}+$ $\frac{3}{5m}$
1. **State the problem:** Simplify the expression $$\frac{4}{3m} + \frac{3}{5m}$$.
2. **Identify the common denominator:** Both fractions have the variable $m$ in the denominator, so the common denominator is $$15m$$ (the least common multiple of $3m$ and $5m$).
3. **Rewrite each fraction with the common denominator:**
$$\frac{4}{3m} = \frac{4 \times 5}{3m \times 5} = \frac{20}{15m}$$
$$\frac{3}{5m} = \frac{3 \times 3}{5m \times 3} = \frac{9}{15m}$$
4. **Add the fractions:**
$$\frac{20}{15m} + \frac{9}{15m} = \frac{20 + 9}{15m} = \frac{29}{15m}$$
5. **Final answer:**
$$\boxed{\frac{29}{15m}}$$
This is the simplified sum of the two fractions.