1. **State the problem:** Simplify the expression $$\frac{h - 21}{2h - 10} + \frac{h + 3}{h - 5}$$. 2. **Rewrite the denominators:** Notice that $$2h - 10 = 2(h - 5)$$. 3. **Rewrite the expression using this factorization:** $$\frac{h - 21}{2(h - 5)} + \frac{h + 3}{h - 5}$$ 4. **Find a common denominator:** The common denominator is $$2(h - 5)$$. 5. **Rewrite the second fraction to have the common denominator:** $$\frac{h + 3}{h - 5} = \frac{2(h + 3)}{2(h - 5)}$$ 6. **Add the fractions:** $$\frac{h - 21}{2(h - 5)} + \frac{2(h + 3)}{2(h - 5)} = \frac{h - 21 + 2(h + 3)}{2(h - 5)}$$ 7. **Simplify the numerator:** $$h - 21 + 2h + 6 = 3h - 15$$ 8. **Rewrite the expression:** $$\frac{3h - 15}{2(h - 5)}$$ 9. **Factor the numerator:** $$3h - 15 = 3(h - 5)$$ 10. **Simplify the fraction by canceling common factors:** $$\frac{\cancel{3}(h - 5)}{2\cancel{(h - 5)}} = \frac{3}{2}$$ **Final answer:** $$\frac{3}{2}$$