Question

3x-5/x-1 -2x-5/x-2=1

Answer 1

Ответ: х=3

$\frac{3x - 5}{x - 1} - \frac{2x - 5}{x - 2} = 1$

ОДЗ: х-1≠0 х≠1

х-2≠0 х≠2

$\frac{(x - 2) \times (3x - 5) - (x - 1) \times (2x - 5)}{(x - 1) \times (x - 2)} = 1$

$\frac{3 {x}^{2} - 5x - 6x + 10 - (2 {x}^{2} - 5x - 2x + 5) }{(x - 1)(x - 2)} = 1$

$\frac{3 {x}^{2} - 5x - 6x + 10 - 2 {x}^{2} + 7x - 5 }{(x - 1)(x - 2)}$

$\frac{ {x}^{2} - 4x + 5 }{(x - 1)(x - 2)}$

${x}^{2} - 4x + 5 = (x - 1)(x - 2)$

${x}^{2} - 4x + 5 = {x}^{2} - 2x - x + 2$

$- 4x + 5 = - 2x - x + 2$

$- 4x + 5 = - 3x + 2$

$- 4x + 3x = 2 - 5$

$- x = - 3$

$x = 3$