Question

Найди корень уравнения

Answer 1

$\frac{2s - 6}{ {s}^{2} - 9} - \frac{s - 6}{ {s}^{2} - 3s} = \frac{s - 1}{ {s}^{2} + 3s } \\ \frac{2(s - 3)}{(s - 3)(s + 3)} - \frac{s - 6}{ {s}^{2} - 3s} = \frac{s - 1}{ {s}^{2} + 3s} \\ \frac{2}{s + 3} - \frac{s - 6}{ {s}^{2} - 3s } = \frac{s - 1}{ {s}^{2} + 3s } \\ \frac{2}{s + 3} - \frac{s - 6}{ {s}^{2} - 3s } - \frac{s - 1}{ {s}^{2} + 3s } = 0 \\ \frac{2}{s + 3} - \frac{s - 6}{s(s - 3)} - \frac{s - 1}{s(s + 3)} = 0 \\ \frac{2s(s - 3) - (s + 3) \times (s - 6) - (s - 3) \times (s - 1)}{s \times (s - 3)(s + 3)} = 0 \\ \frac{2 {s}^{2} - 6s - ( {s}^{2} - 3s - 18) - ( {s}^{2} - 4s + 3)}{s \times (s - 3)(s + 3)} = 0 \\ \frac{0 + s + 15}{s \times (s - 3)(s + 3)} = 0 \\ \frac{s + 15}{s \times (s - 3)(s + 3)} = 0 \\ s + 15 = 0 \\ s = - 15$