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

May 27, 2015

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

cross multiplying

$x \left(x - 2\right) = 3$
${x}^{2} - 2 x = 3$
${x}^{2} - 2 x - 3 = 0$

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

the solutions for the equation are color(red)(x=-1 and x=3