Precalculus Examples

$f (x) = \frac{2}{x} + \frac{4}{x + 1}$

Step 1

Set the denominator in $\frac{2}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{4}{x + 1}$ equal to $0$ to find where the expression is undefined.

$x + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 4

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

Interval Notation:

$(- \infty, - 1) \cup (- 1, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 1}$

Step 5