1. **State the problem:** Simplify the expression $$\frac{\frac{1}{3} + \frac{1}{4}}{\frac{1}{5} + \frac{1}{6}}$$. 2. **Recall the formula:** To add fractions, use $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$. 3. **Calculate the numerator:** $$\frac{1}{3} + \frac{1}{4} = \frac{1 \times 4 + 1 \times 3}{3 \times 4} = \frac{4 + 3}{12} = \frac{7}{12}$$. 4. **Calculate the denominator:** $$\frac{1}{5} + \frac{1}{6} = \frac{1 \times 6 + 1 \times 5}{5 \times 6} = \frac{6 + 5}{30} = \frac{11}{30}$$. 5. **Divide the numerator by the denominator:** $$\frac{\frac{7}{12}}{\frac{11}{30}} = \frac{7}{12} \times \frac{30}{11} = \frac{7 \times 30}{12 \times 11} = \frac{210}{132}$$. 6. **Simplify the fraction:** Find the greatest common divisor (GCD) of 210 and 132, which is 6. $$\frac{210 \div 6}{132 \div 6} = \frac{35}{22}$$. **Final answer:** $$\frac{35}{22}$$.