Precalculus Examples

$f (x) = \frac{1}{x} + \frac{5}{x - 3}$

Step 1

Set the denominator in $\frac{1}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{5}{x - 3}$ equal to $0$ to find where the expression is undefined.

$x - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$x = 3$

Step 4

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

Interval Notation:

$(- \infty, 0) \cup (0, 3) \cup (3, \infty)$

Set-Builder Notation:

${x | x \neq 0, 3}$

Step 5