Find the Domain ( square root of x)/(x-18)

$\frac{\sqrt{x}}{x - 18}$

Step 1

Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 2

Set the denominator in $\frac{\sqrt{x}}{x - 18}$ equal to $0$ to find where the expression is undefined.

$x - 18 = 0$

Step 3

Add $18$ to both sides of the equation.

$x = 18$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, 18) \cup (18, \infty)$

Set-Builder Notation:

${x | x \geq 0, x \neq 18}$

Step 5