Precalculus Examples

$g (x) = \frac{1}{x} - \frac{3}{x + 2}$

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 $\frac{3}{x + 2}$ equal to $0$ to find where the expression is undefined.

$x + 2 = 0$

Step 3

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 4

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

Interval Notation:

$(- \infty, - 2) \cup (- 2, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 2}$

Step 5