80. \( \frac{x^{2}-x-2}{x^{2}-7 x+10} \div \frac{x^{2}-3 x-4}{40-3 x-x^{2}} \)

To simplify the expression: \[ \frac{x^{2} - x - 2}{x^{2} - 7x + 10} \div \frac{x^{2} - 3x - 4}{40 - 3x - x^{2}} \] we follow these steps: 1. **Rewrite the Division as Multiplication:** \[ \frac{x^{2} - x - 2}{x^{2} - 7x + 10} \times \frac{40 - 3x - x^{2}}{x^{2} - 3x - 4} \] 2. **Factor Each Polynomial:** - **Factor \(x^{2} - x - 2\):** \[ x^{2} - x - 2 = (x - 2)(x + 1) \] - **Factor \(x^{2} - 7x + 10\):** \[ x^{2} - 7x + 10 = (x - 2)(x - 5) \] - **Factor \(x^{2} - 3x - 4\):** \[ x^{2} - 3x - 4 = (x - 4)(x + 1) \] - **Factor \(40 - 3x - x^{2}\):** \[ 40 - 3x - x^{2} = -x^{2} - 3x + 40 = -(x^{2} + 3x - 40) = -(x + 8)(x - 5) \] 3. **Substitute the Factors Back into the Expression:** \[ \frac{(x - 2)(x + 1)}{(x - 2)(x - 5)} \times \frac{-(x + 8)(x - 5)}{(x - 4)(x + 1)} \] 4. **Cancel Common Factors:** - \( (x - 2) \) cancels out. - \( (x + 1) \) cancels out. - \( (x - 5) \) cancels out. This leaves: \[ \frac{- (x + 8)}{(x - 4)} \] 5. **Final Simplified Form:** \[ \frac{-(x + 8)}{x - 4} \] **Answer:** After simplifying, the expression is –(x + 8) divided by (x – 4). Thus, −(x+8)/(x−4)