# How do you find the domain of y=(2x)/(x+9)?

Oct 3, 2016

$x \ne - 9$ or interval notation $\left(- \infty , - 9\right) U \left(- 9 , \infty\right)$

#### Explanation:

If a value of $x$ results in $y$ being "undefined", that value of $x$ is not included in the domain. The domain is the allowed values of $x$.

For a rational equation like this example, dividing by zero will result in an undefined $y$. So, the denominator should not equal zero.

$x + 9 \ne \textcolor{w h i t e}{a} 0$
$\textcolor{w h i t e}{a} - 9 \textcolor{w h i t e}{a a} - 9$

$x \ne - 9$

A value of $- 9$ will result in a zero in the denominator, so $- 9$ is not be included in the domain.

In interval notation, this is written as $\left(- \infty , - 9\right) U \left(- 9 , \infty\right)$