How do you solve the rational equation (x-2)/3=1/x?

Jan 1, 2016

$x = 3 \text{ }$ or $\text{ } x = - 1$

Explanation:

Cross multiply to get

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

Rearrange to get

${x}^{2} - 2 x - 3 = 0$

Factor to get

$\left(x - 3\right) \left(x + 1\right) = 0$

$\left\{\begin{matrix}x - 3 = 0 \\ x + 1 = 0\end{matrix}\right. \implies \left\{\begin{matrix}x = 3 \\ x = - 1\end{matrix}\right.$