Question

решите уравнение 1/x-1=x-3/1-x

Answer 1

Ответ:

x = 2

Объяснение:

$\frac{1}{x - 1} = \frac{x - 3}{1 - x}$

1 - x = (x - 3) × (x - 1)

1 - x - (x² - x - 3x + 3) = 0

1 - x - x² + 4x - 3 = 0

-x² + 3x - 2 = 0

x² - 3x + 2 = 0

x² - x - 2x + 2 = 0

x × (x - 1) - 2 (x - 1) = 0

(x - 1) × (x - 2) = 0

x = 2