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

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

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

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

The formula of factoring:

(x - x_1)(x - x_2)

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

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