Precalculus Examples

$\frac{5}{\frac{x}{x + 5}}$

Step 1

Set the denominator in $\frac{x}{x + 5}$ equal to $0$ to find where the expression is undefined.

$x + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 3

Set the denominator in $\frac{5}{\frac{x}{x + 5}}$ equal to $0$ to find where the expression is undefined.

$\frac{x}{x + 5} = 0$

Step 4

Set the numerator equal to zero.

$x = 0$

Step 5

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

Interval Notation:

$(- \infty, - 5) \cup (- 5, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 5}$

Step 6