1. **State the problem:** Simplify the expression $$\frac{\left(-\frac{2}{5}\right) + \left(\frac{1}{-2}\right)}{\left(\frac{5}{-8}\right) - \left(-\frac{1}{2}\right)}$$. 2. **Rewrite the expression clearly:** $$\frac{-\frac{2}{5} - \frac{1}{2}}{-\frac{5}{8} + \frac{1}{2}}$$ 3. **Find a common denominator for the numerator:** The denominators are 5 and 2, so the common denominator is 10. $$-\frac{2}{5} = -\frac{4}{10}, \quad -\frac{1}{2} = -\frac{5}{10}$$ 4. **Add the fractions in the numerator:** $$-\frac{4}{10} - \frac{5}{10} = -\frac{9}{10}$$ 5. **Find a common denominator for the denominator:** The denominators are 8 and 2, so the common denominator is 8. $$-\frac{5}{8} = -\frac{5}{8}, \quad \frac{1}{2} = \frac{4}{8}$$ 6. **Add the fractions in the denominator:** $$-\frac{5}{8} + \frac{4}{8} = -\frac{1}{8}$$ 7. **Rewrite the entire expression:** $$\frac{-\frac{9}{10}}{-\frac{1}{8}}$$ 8. **Divide the fractions by multiplying by the reciprocal:** $$-\frac{9}{10} \times -\frac{8}{1}$$ 9. **Multiply numerators and denominators:** $$\frac{(-9) \times (-8)}{10 \times 1} = \frac{72}{10}$$ 10. **Simplify the fraction:** $$\frac{72}{10} = \frac{\cancel{72}^{\times 6}}{\cancel{10}^{\times 5}} = \frac{36}{5}$$ **Final answer:** $$\frac{36}{5}$$