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

Apr 10, 2016

$x = 3$ or $x = - 1$.

#### Explanation:

Cross Multiply:

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

$x \left(x - 2\right) = 3$

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

What we now have is a quadratic equation:
We can now factor this further:

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

Now we can solve by using the null factor law (that is, determining the numbers that make each bracket =0):

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

Solution 1:
$\textcolor{red}{\left(3 - 3\right)} \left(3 + 1\right) = 0$
$0 \cdot 4 = 0$
$0 = 0$
Therefore, one solution to the equation is $x = 3$

Solution 2:
$\left(1 - 3\right) \textcolor{red}{\left(- 1 + 1\right)} = 0$
$- 2 \cdot 0 = 0$
$0 = 0$
Therefore, the other solution to the equation is $x - 1$

Therefore, $x = 3$ or $x = - 1$.