Question

СРОЧНО
Решите уравнение: $frac{5x+7}{x^{2} - 11x-12} = frac{13x-1}{x*(x-11) - 12}$

Answer 1

$displaystyle frac{5x + 7}{ {x}^{2} - 11x - 12} = frac{13x - 1}{x times (x - 11) - 12} \ \ \ frac{5x + 7}{ {x}^{2} - 11x - 12} = frac{13x - 1}{ {x}^{2} - 11x - 12 } \ \ \ frac{5x + 7}{ {x}^{2} - 11x - 12} - frac{13x - 1}{ {x}^{2} - 11x - 12 } = 0 \ \ \ frac{5x + 7 - 13x + 1}{ { x}^{2} - 11x - 12} = 0$

x² - 11x - 12 ≠ 0 (на ноль делить нельзя)

D = 121 - 4 * (-12) = 121 + 48 = 169

$x1 = displaystyle frac{11 + 13}{2} = frac{24}{2} = 12 \ \ \ x2 = frac{11 - 13}{2} = frac{ - 2}{2} = - 1$

x ≠ 12

x ≠ -1

5x + 7 - 13x + 1 = 0

-8x + 8 = 0

-8x = -8

x = -8/-8 = 1

Ответ: x = 1