Finite Math Examples

$\frac{1}{\sqrt[3]{3} - 1}$

Step 1

Multiply $\frac{1}{\sqrt[3]{3} - 1}$ by $\frac{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}$ .

$\frac{1}{\sqrt[3]{3} - 1} \cdot \frac{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}$

Step 2

Combine fractions.

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Step 2.1

Multiply $\frac{1}{\sqrt[3]{3} - 1}$ by $\frac{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}$ .

$\frac{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{(\sqrt[3]{3} - 1) ({\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2})}$

Step 2.2

Expand the denominator using the FOIL method.

$\frac{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{{\sqrt[3]{3}}^{3} + {\sqrt[3]{3}}^{2} + \sqrt[3]{3} {(- 1)}^{2} - {\sqrt[3]{3}}^{2} - \sqrt[3]{3} + {(- 1)}^{3}}$

Step 2.3

Simplify.

$\frac{{\sqrt[3]{3}}^{2} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[3]{3}}^{2}$ as $\sqrt[3]{3^{2}}$ .

$\frac{\sqrt[3]{3^{2}} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{2}$

Step 3.2

Raise $3$ to the power of $2$ .

$\frac{\sqrt[3]{9} - \sqrt[3]{3} \cdot - 1 + {(- 1)}^{2}}{2}$

Step 3.3

Multiply $- \sqrt[3]{3} \cdot - 1$ .

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Step 3.3.1

Multiply $- 1$ by $- 1$ .

$\frac{\sqrt[3]{9} + 1 \sqrt[3]{3} + {(- 1)}^{2}}{2}$

Step 3.3.2

Multiply $\sqrt[3]{3}$ by $1$ .

$\frac{\sqrt[3]{9} + \sqrt[3]{3} + {(- 1)}^{2}}{2}$

Step 3.4

Raise $- 1$ to the power of $2$ .

$\frac{\sqrt[3]{9} + \sqrt[3]{3} + 1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[3]{9} + \sqrt[3]{3} + 1}{2}$

Decimal Form:

$2.26116669 \dots$