# How do you solve  (x-2) / 3=1 / x?

$\frac{x - 2}{3} = \frac{1}{x} \implies x \left(x - 2\right) = 3 \implies {x}^{2} - 2 x - 3 = 0 \implies \left({x}^{2} - 2 x + 1\right) - 4 = 0 \implies {\left(x - 1\right)}^{2} - {2}^{2} = 0 \implies \left[x - 1 - 2\right] \cdot \left[x - 1 + 2\right] = 0 \implies \left(x - 3\right) \cdot \left(x + 1\right) = 0 \implies x = 3 \mathmr{and} x = - 1$