# How do you solve rational equations 2/x-2 = x/(x-1) - 2?

Apr 30, 2018

No solutions

#### Explanation:

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

$2 \left(x - 1\right) = {x}^{2}$

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

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

Use the formula

$x = \frac{- \left(- 2\right) \setminus \pm \sqrt{{\left(- 2\right)}^{2} - 4 \times 1 \times 2}}{2}$

$x = \frac{2 \setminus \pm \sqrt{- 4}}{2}$

Cannot find the square root of a negative number so there are no solutions.