Question

Решите уравнение 5x-3/x-3=2x-3/x

Answer 1

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