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

May 27, 2015

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

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

cross multiplying:
$x \left(x - 2\right) = 1.3$
${x}^{2} - 2 x = 3$
${x}^{2} - 2 x - 3 = 0$

Factorising the term to find solutions:

Splitting the middle term:
${x}^{2} - 3 x + x - 3 = 0$
$x \left(x - 3\right) + 1 \left(x - 3\right) = 0$

the solutions are color(blue)(x = -1 , x=3