1. **State the problem:** Simplify the expression $$\frac{2m - 10}{m^2 - 5m - 24} + \frac{4m + 28}{m^2 - 5m - 24}$$ where both fractions have the same denominator. 2. **Formula and rules:** When adding fractions with the same denominator, add the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$$ 3. **Add the numerators:** $$\frac{(2m - 10) + (4m + 28)}{m^2 - 5m - 24} = \frac{2m - 10 + 4m + 28}{m^2 - 5m - 24}$$ 4. **Simplify the numerator:** $$2m + 4m = 6m$$ $$-10 + 28 = 18$$ So, $$\frac{6m + 18}{m^2 - 5m - 24}$$ 5. **Factor numerator and denominator:** Numerator: $$6m + 18 = 6(m + 3)$$ Denominator: $$m^2 - 5m - 24$$ Find factors of -24 that sum to -5: -8 and +3 $$m^2 - 5m - 24 = (m - 8)(m + 3)$$ 6. **Rewrite the fraction:** $$\frac{6(m + 3)}{(m - 8)(m + 3)}$$ 7. **Cancel common factors:** $$\frac{6\cancel{(m + 3)}}{(m - 8)\cancel{(m + 3)}} = \frac{6}{m - 8}$$ 8. **Final answer:** $$\boxed{\frac{6}{m - 8}}$$ This is the simplified form of the original expression.