1. **State the problem:** Simplify the expression $$\frac{2y - 8}{y^2 - 3y - 4} + \frac{3}{y + 1}$$. 2. **Factor the denominators and numerator where possible:** - Factor the quadratic in the denominator: $$y^2 - 3y - 4 = (y - 4)(y + 1)$$. - Factor the numerator of the first fraction: $$2y - 8 = 2(y - 4)$$. 3. **Rewrite the expression with factored forms:** $$\frac{2(y - 4)}{(y - 4)(y + 1)} + \frac{3}{y + 1}$$ 4. **Simplify the first fraction by canceling common factors:** $$\frac{\cancel{2}(y - 4)}{\cancel{(y - 4)}(y + 1)} = \frac{2}{y + 1}$$ 5. **Now the expression is:** $$\frac{2}{y + 1} + \frac{3}{y + 1}$$ 6. **Since denominators are the same, add the numerators:** $$\frac{2 + 3}{y + 1} = \frac{5}{y + 1}$$ 7. **Check if this matches any answer choice:** The simplified form is $$\frac{5}{y + 1}$$, which is not exactly any of the given options. 8. **Re-examine the problem:** The original expression was $$\frac{2y - 8}{y^2 - 3y - 4} + \frac{3}{y + 1}$$. 9. **Try to combine the fractions before canceling:** Common denominator is $$(y - 4)(y + 1)$$. 10. **Rewrite the second fraction with common denominator:** $$\frac{3}{y + 1} = \frac{3(y - 4)}{(y + 1)(y - 4)}$$ 11. **Add the two fractions:** $$\frac{2(y - 4) + 3(y - 4)}{(y - 4)(y + 1)} = \frac{(2 + 3)(y - 4)}{(y - 4)(y + 1)} = \frac{5(y - 4)}{(y - 4)(y + 1)}$$ 12. **Cancel the common factor $(y - 4)$:** $$\frac{\cancel{5}(y - 4)}{\cancel{(y - 4)}(y + 1)} = \frac{5}{y + 1}$$ 13. **This confirms the simplified form is:** $$\frac{5}{y + 1}$$ 14. **Check the answer choices again:** None of the options exactly match $$\frac{5}{y + 1}$$. 15. **Check if the given answer choice (2y - 5) / (y^2 - 2y - 3) can be simplified to the same:** - Factor denominator: $$y^2 - 2y - 3 = (y - 3)(y + 1)$$. - The numerator is $$2y - 5$$, which does not factor nicely. 16. **Conclusion:** The simplified form of the original expression is $$\frac{5}{y + 1}$$. **Final answer:** $$\boxed{\frac{5}{y + 1}}$$