# How do you find the domain of g(x)= x/(x^2-5x)?

Oct 25, 2017

$x \in \mathbb{R} , x \ne 0 , 5$

#### Explanation:

The domain is the range of $x$ values a function can take.

The numerator of $g \left(x\right)$ is simply $x$ so it doesn't really matter what it is.

The denominator is more complex because we know that we can never divide by $0$.

If the denominator is $0$, then

${x}^{2} - 5 x = 0$

$x \left(x - 5\right) = 0$

so

$x = 0 , 5$

In which case the domain is $x \in \mathbb{R} , x \ne 0 , 5$