Precalculus Examples

$\frac{y}{y - 6} + \frac{15}{y + 6}$

Step 1

Set the denominator in $\frac{y}{y - 6}$ equal to $0$ to find where the expression is undefined.

$y - 6 = 0$

Step 2

Add $6$ to both sides of the equation.

$y = 6$

Step 3

Set the denominator in $\frac{15}{y + 6}$ equal to $0$ to find where the expression is undefined.

$y + 6 = 0$

Step 4

Subtract $6$ from both sides of the equation.

$y = - 6$

Step 5

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

Interval Notation:

$(- \infty, - 6) \cup (- 6, 6) \cup (6, \infty)$

Set-Builder Notation:

${y | y \neq 6, - 6}$

Step 6