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