1. **State the problem:** Divide $\left(1\frac{1}{2} + \frac{1}{4}\right)$ by $\left(1\frac{1}{2} - \frac{1}{4}\right)$. 2. **Convert mixed numbers to improper fractions:** $1\frac{1}{2} = \frac{3}{2}$. 3. **Rewrite the expression:** $$\frac{\frac{3}{2} + \frac{1}{4}}{\frac{3}{2} - \frac{1}{4}}$$ 4. **Find common denominators and add/subtract fractions:** For the numerator: $$\frac{3}{2} + \frac{1}{4} = \frac{6}{4} + \frac{1}{4} = \frac{7}{4}$$ For the denominator: $$\frac{3}{2} - \frac{1}{4} = \frac{6}{4} - \frac{1}{4} = \frac{5}{4}$$ 5. **Divide the fractions:** $$\frac{\frac{7}{4}}{\frac{5}{4}} = \frac{7}{4} \times \frac{4}{5} = \frac{7 \times 4}{4 \times 5} = \frac{7}{5}$$ 6. **Simplify the result:** $$\frac{7}{5} = 1\frac{2}{5}$$ **Final answer:** $$1\frac{2}{5}$$