Precalculus Examples

$f (x) = \frac{1}{x + 7} + \frac{3}{x - 9}$

Step 1

Set the denominator in $\frac{1}{x + 7}$ equal to $0$ to find where the expression is undefined.

$x + 7 = 0$

Step 2

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 3

Set the denominator in $\frac{3}{x - 9}$ equal to $0$ to find where the expression is undefined.

$x - 9 = 0$

Step 4

Add $9$ to both sides of the equation.

$x = 9$

Step 5

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

Interval Notation:

$(- \infty, - 7) \cup (- 7, 9) \cup (9, \infty)$

Set-Builder Notation:

${x | x \neq - 7, 9}$

Step 6