Precalculus Examples

$\frac{32}{y} - \frac{y + 1}{y + 7}$

Step 1

Set the denominator in $\frac{32}{y}$ equal to $0$ to find where the expression is undefined.

$y = 0$

Step 2

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

$y + 7 = 0$

Step 3

Subtract $7$ from both sides of the equation.

$y = - 7$

Step 4

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

Interval Notation:

$(- \infty, - 7) \cup (- 7, 0) \cup (0, \infty)$

Set-Builder Notation:

${y | y \neq 0, - 7}$

Step 5