1. **State the problem:** Add the expressions $$- \frac{7}{x^2 + 3x - 10} + \frac{12}{x^2 - 2x - 35}$$. 2. **Factor the denominators:** $$x^2 + 3x - 10 = (x + 5)(x - 2)$$ $$x^2 - 2x - 35 = (x - 7)(x + 5)$$ 3. **Find the common denominator:** The least common denominator (LCD) is $$ (x + 5)(x - 2)(x - 7) $$. 4. **Rewrite each fraction with the LCD:** $$- \frac{7}{(x + 5)(x - 2)} = - \frac{7(x - 7)}{(x + 5)(x - 2)(x - 7)}$$ $$\frac{12}{(x - 7)(x + 5)} = \frac{12(x - 2)}{(x + 5)(x - 2)(x - 7)}$$ 5. **Add the numerators:** $$-7(x - 7) + 12(x - 2) = -7x + 49 + 12x - 24 = 5x + 25$$ 6. **Write the combined fraction:** $$\frac{5x + 25}{(x + 5)(x - 2)(x - 7)}$$ 7. **Factor numerator:** $$5x + 25 = 5(x + 5)$$ 8. **Simplify by canceling common factor:** $$\frac{\cancel{5}(x + 5)}{(x + 5)(x - 2)(x - 7)} = \frac{5}{(x - 2)(x - 7)}$$ 9. **Rewrite denominator as quadratic:** $$(x - 2)(x - 7) = x^2 - 9x + 14$$ 10. **Final answer:** $$\frac{5}{x^2 - 9x + 14}$$ This matches option B.