Question

Simplify 2x^2-7x-4 / x2-5x+4 edge2020

Answer 1

`\frac{2 {x}^(2) - 7x - 4}{ {x}^(2) - 5x + 4} \\`

1)

`2 {x}^(2) - 7x - 4 = 0 \\ D=( - 7) ^(2) - 4 * 2 * ( - 4) = 81 = {9}^(2) \\ x_1 = (7 + 9)/(4) = 4 \\ x_2 = (7 - 9)/(4) = - 0.5`

2)

`{x}^(2) - 5x + 4 = 0 \\ D = ( - 5) ^(2) - 4 * 4 = 9 = {3}^(2) \\x_1 = (5 + 3)/(2) = 4 \\ x_2 = (5 - 3)/(2) = 1`

3)

The formula of factoring:

`(x - x_1)(x - x_2)`

4)

`\frac{2 {x}^(2) - 7x - 4}{ {x}^(2) - 5x + 4} = ((x - 4)(x + 0.5))/((x - 4)(x - 1)) = (x + 0.5)/(x - 1) \\`