Precalculus Examples

$g (x) = \frac{6}{x + 3} + \frac{2}{x - 4}$

Step 1

Set the denominator in $\frac{6}{x + 3}$ equal to $0$ to find where the expression is undefined.

$x + 3 = 0$

Step 2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 3

Set the denominator in $\frac{2}{x - 4}$ equal to $0$ to find where the expression is undefined.

$x - 4 = 0$

Step 4

Add $4$ to both sides of the equation.

$x = 4$

Step 5

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

Interval Notation:

$(- \infty, - 3) \cup (- 3, 4) \cup (4, \infty)$

Set-Builder Notation:

${x | x \neq - 3, 4}$

Step 6