Question

Решите уравнение 5x-3/x-3=2x-3/x

Answer 1

$\frac{5x - 3}{x - 3} = \frac{2x - 3}{x} |(x - 3)x \\ (5x - 3)x - (2x - 3)(x - 3) = 0 \\ 5x {}^{2} - 3x - (2x {}^{2} - 6x - 3x + 9) = 0 \\ 5 x {}^{2} - 3x - 2x {}^{2} + 9x - 9 = 0 \\ 3x {}^{2} + 6x - 9 = 0 \\ x {}^{2} + 2x - 3 = 0 \\ x = \frac{ - 2 + \sqrt{2 {}^{2} - 4 \times 1 \times ( - 3)} }{2} = \sqrt{16} = 4 \\ x1 = \frac{ - 2 + 4}{2} = 1 \\ x2 = \frac{ - 2 - 4}{2} = - 3$