# How do you solve and write the following in interval notation: (x-6)^2/x<0??

Mar 31, 2017

$x$ lies in the interval $\left(- \infty , 0\right)$

#### Explanation:

The inequality ${\left(x - 6\right)}^{2} / x < 0$, means ${\left(x - 6\right)}^{2} / x$ is negative.

As the numerator ${\left(x - 6\right)}^{2}$ is always positive,

${\left(x - 6\right)}^{2} / x$ is negative only if $x$ is negative i.e. $x < 0$

i.e. $x$ lies in the interval $\left(- \infty , 0\right)$