Precalculus Examples

$f (x) = \frac{1}{x + 8} + \frac{3}{x - 10}$

Step 1

Set the denominator in $\frac{1}{x + 8}$ equal to $0$ to find where the expression is undefined.

$x + 8 = 0$

Step 2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 3

Set the denominator in $\frac{3}{x - 10}$ equal to $0$ to find where the expression is undefined.

$x - 10 = 0$

Step 4

Add $10$ to both sides of the equation.

$x = 10$

Step 5

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

Interval Notation:

$(- \infty, - 8) \cup (- 8, 10) \cup (10, \infty)$

Set-Builder Notation:

${x | x \neq - 8, 10}$

Step 6