Question

x/(1-x) + (x-2)/x =1 com U=R
Façam com cálculo por favor

Answer 1

$\frac{x}{1 - x} + \frac{x - 2}{x} = 1$

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

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

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

$3x - 2 = x - {x}^{2}$

${x}^{2} + 2x - 2 = 0$

$x = \frac{-2 + - \sqrt{{2}^{2} - 4 \times 1 \times (-2)}}{2}$

$x = \frac{-2 + - \sqrt{4+8}}{2}$

$x = \frac{-2 + - 2\sqrt{3}}{2}$

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

ou

$x= -1 +\sqrt{3}$