Calculus Examples

$\frac{\sqrt[3]{x - 5}}{x^{3} - 5}$

Step 1

Set the denominator in $\frac{\sqrt[3]{x - 5}}{x^{3} - 5}$ equal to $0$ to find where the expression is undefined.

$x^{3} - 5 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $5$ to both sides of the equation.

$x^{3} = 5$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{5}$

Step 3

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

Interval Notation:

$(- \infty, \sqrt[3]{5}) \cup (\sqrt[3]{5}, \infty)$

Set-Builder Notation:

${x | x \neq \sqrt[3]{5}}$

Step 4