Algebra Examples

$\frac{2}{\sqrt[3]{4} - 3}$

Step 1

Multiply $\frac{2}{\sqrt[3]{4} - 3}$ by $\frac{{\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2}}{{\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2}}$ .

$\frac{2}{\sqrt[3]{4} - 3} \cdot \frac{{\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2}}{{\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2}}$

Step 2

Combine fractions.

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Step 2.1

Multiply $\frac{2}{\sqrt[3]{4} - 3}$ by $\frac{{\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2}}{{\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2}}$ .

$\frac{2 ({\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{(\sqrt[3]{4} - 3) ({\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}$

Step 2.2

Expand the denominator using the FOIL method.

$\frac{2 ({\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{{\sqrt[3]{4}}^{3} + 3 {\sqrt[3]{4}}^{2} + \sqrt[3]{4} {(- 3)}^{2} - 3 {\sqrt[3]{4}}^{2} - 9 \sqrt[3]{4} + {(- 3)}^{3}}$

Step 2.3

Simplify.

$\frac{2 ({\sqrt[3]{4}}^{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{- 23}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[3]{4}}^{2}$ as $\sqrt[3]{4^{2}}$ .

$\frac{2 (\sqrt[3]{4^{2}} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{- 23}$

Step 3.2

Raise $4$ to the power of $2$ .

$\frac{2 (\sqrt[3]{16} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{- 23}$

Step 3.3

Rewrite $16$ as $2^{3} \cdot 2$ .

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Step 3.3.1

Factor $8$ out of $16$ .

$\frac{2 (\sqrt[3]{8 (2)} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{- 23}$

Step 3.3.2

Rewrite $8$ as $2^{3}$ .

$\frac{2 (\sqrt[3]{2^{3} \cdot 2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{- 23}$

Step 3.4

Pull terms out from under the radical.

$\frac{2 (2 \sqrt[3]{2} - \sqrt[3]{4} \cdot - 3 + {(- 3)}^{2})}{- 23}$

Step 3.5

Multiply $- 3$ by $- 1$ .

$\frac{2 (2 \sqrt[3]{2} + 3 \sqrt[3]{4} + {(- 3)}^{2})}{- 23}$

Step 3.6

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

$\frac{2 (2 \sqrt[3]{2} + 3 \sqrt[3]{4} + 9)}{- 23}$

Step 4

Move the negative in front of the fraction.

$- \frac{2 (2 \sqrt[3]{2} + 3 \sqrt[3]{4} + 9)}{23}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 (2 \sqrt[3]{2} + 3 \sqrt[3]{4} + 9)}{23}$

Decimal Form:

$- 1.41583002 \dots$