[tex] \frac{2 {x}^{2} - 7x - 4}{ {x}^{2} - 5x + 4} \\ [/tex]
1)
[tex]2 {x}^{2} - 7x - 4 = 0 \\ D=( - 7) ^{2} - 4 \times 2 \times ( - 4) = 81 = {9}^{2} \\ x_1 = \frac{7 + 9}{4} = 4 \\ x_2 = \frac{7 - 9}{4} = - 0.5[/tex]
2)
[tex] {x}^{2} - 5x + 4 = 0 \\ D = ( - 5) ^{2} - 4 \times 4 = 9 = {3}^{2} \\x_1 = \frac{5 + 3}{2} = 4 \\ x_2 = \frac{5 - 3}{2} = 1[/tex]
3)
The formula of factoring:
[tex](x - x_1)(x - x_2)[/tex]
4)
[tex] \frac{2 {x}^{2} - 7x - 4}{ {x}^{2} - 5x + 4} = \frac{(x - 4)(x + 0.5)}{(x - 4)(x - 1)} = \frac{x + 0.5}{x - 1} \\ [/tex]
