# How do you find the domain of 5/(x sqrt (x+2))?

Jun 16, 2018

The domain is $x \in \left(- 2 , 0\right) \cup \left(0 , + \infty\right)$

#### Explanation:

The denominator must be $\ne 0$

Therefore,

$x \ne 0$

and

$x + 2 \ne 0$, $\implies$, $x \ne - 2$

and for the square root sign

$x + 2 > 0$, $\implies$, $x > - 2$

Finally. the domain is $x \in \left(- 2 , 0\right) \cup \left(0 , + \infty\right)$

graph{5/(xsqrt(x+2)) [-20.28, 20.27, -10.14, 10.14]}