[tex]x {}^{2} - x - 2 = 0 \\ x_{1} + x _{2} =1 \\ x_{1} \times x _{2} = - 2 \\ x_{1} = 2\\ x _{2} = - 1 \\ {x}^{2} - x - 2 = (x + 1)(x - 2)[/tex]

[tex]3 {x}^{2} - 5x - 2 = 0 \\ d = ( - 5) {}^{2} - 4 \times 3 \times ( - 2) = \\ 25 + 24 = 49 \\ x_{1} = \frac{5 + 7}{2 \times 3} = \frac{12}{6} = 2 \\ x _{2} = \frac{5 - 7}{2 \times 3} = - \frac{2}{6} = - \frac{1}{3} \\ 3 {x}^{2} - 5x - 2 = 3(x - 2)(x + \frac{1}{3} ) = \\ (x -2 )(3x + 1)[/tex]

[tex] \frac{ {x}^{2} - x - 2}{3 {x}^{2} - 5x - 2 } = \frac{(x - 2)(x + 1)}{(x - 2)(3x + 1)} = \frac{x + 1}{3x + 1} [/tex]