Calculus Examples

$\frac{z^{2} - 9}{z} \div \frac{z + 3}{z - 3}$

Step 1

Set the denominator in $\frac{z^{2} - 9}{z}$ equal to $0$ to find where the expression is undefined.

$z = 0$

Step 2

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

$z - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$z = 3$

Step 4

Set the denominator in $\frac{z^{2} - 9}{z} \div \frac{z + 3}{z - 3}$ equal to $0$ to find where the expression is undefined.

$\frac{z + 3}{z - 3} = 0$

Step 5

Solve for $z$ .

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Step 5.1

Set the numerator equal to zero.

$z + 3 = 0$

Step 5.2

Subtract $3$ from both sides of the equation.

$z = - 3$

Step 6

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

Interval Notation:

$(- \infty, - 3) \cup (- 3, 0) \cup (0, 3) \cup (3, \infty)$

Set-Builder Notation:

${z | z \neq 0, 3, - 3}$

Step 7