Trigonometry Examples

$\frac{x^{3 + 4 x}}{x^{4 - 1}}$

Step 1

Set the denominator in $\frac{x^{3 + 4 x}}{x^{4 - 1}}$ equal to $0$ to find where the expression is undefined.

$x^{4 - 1} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $1$ from $4$ .

$x^{3} = 0$

Step 2.2

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

$x = \sqrt[3]{0}$

Step 2.3

Simplify $\sqrt[3]{0}$ .

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Step 2.3.1

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

Step 2.3.2

Pull terms out from under the radical, assuming real numbers.

$x = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 0}$

Step 4