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 \( \frac{x^{2}-x-2}{x^{2}-7x+10} \div \frac{x^{2}-3x-4}{40-3x-x^{2}} \), let's first factor the polynomials involved. 1. **Factoring the first polynomial:** \( x^{2} - x - 2 = (x - 2)(x + 1) \) \( x^{2} - 7x + 10 = (x - 2)(x - 5) \) 2. **Factoring the second polynomial:** \( x^{2} - 3x - 4 = (x - 4)(x + 1) \) The polynomial \( 40 - 3x - x^{2} \) can be rewritten as \( -x^{2} - 3x + 40 \) or just \(- (x^{2} + 3x - 40)\). This can be factored as: \( x^{2} + 3x - 40 = (x + 8)(x - 5) \) Thus, \( 40 - 3x - x^{2} = - (x + 8)(x - 5) \). Now, rewriting the expression using the factored forms: \[ \frac{(x - 2)(x + 1)}{(x - 2)(x - 5)} \div \frac{(x - 4)(x + 1)}{- (x + 8)(x - 5)} \] This division can be transformed into multiplication by flipping the second fraction: \[ = \frac{(x - 2)(x + 1)}{(x - 2)(x - 5)} \cdot \frac{- (x + 8)(x - 5)}{(x - 4)(x + 1)} \] Next, we can cancel out where possible. The \( (x - 2) \) cancels with itself and \( (x - 5) \) also cancels out: \[ = \frac{-(x + 8)}{(x - 4)} \cdot 1 = -\frac{x + 8}{x - 4} \] Conclusively, the simplified expression is: \[ \boxed{-\frac{x + 8}{x - 4}} \]