Pre-Algebra Examples

$\frac{3 - \sqrt[3]{3 x + 3}}{a (\sqrt[3]{x} - 2)}$

Step 1

Factor $3$ out of $3 x + 3$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 - \sqrt[3]{3 (x) + 3}}{a (\sqrt[3]{x} - 2)}$

Step 1.2

Factor $3$ out of $3$ .

$\frac{3 - \sqrt[3]{3 (x) + 3 (1)}}{a (\sqrt[3]{x} - 2)}$

Step 1.3

Factor $3$ out of $3 (x) + 3 (1)$ .

$\frac{3 - \sqrt[3]{3 (x + 1)}}{a (\sqrt[3]{x} - 2)}$

Step 2

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

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

Step 3

Combine fractions.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Reorder.

Tap for more steps...

Step 3.2.1

Move $\sqrt[3]{x} - 2$ .

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

Step 3.2.2

Expand the denominator using the FOIL method.

$\frac{(3 - \sqrt[3]{3 (x + 1)}) ({\sqrt[3]{x}}^{2} - \sqrt[3]{x} \cdot - 2 + {(- 2)}^{2})}{a ({\sqrt[3]{x}}^{3} + 2 {\sqrt[3]{x}}^{2} + \sqrt[3]{x} {(- 2)}^{2} - 2 {\sqrt[3]{x}}^{2} - 4 \sqrt[3]{x} + {(- 2)}^{3})}$

Step 3.2.3

Simplify.

Tap for more steps...

Step 3.2.3.1

Subtract $4 \sqrt[3]{x}$ from $4 \sqrt[3]{x}$ .

$\frac{(3 - \sqrt[3]{3 (x + 1)}) ({\sqrt[3]{x}}^{2} - \sqrt[3]{x} \cdot - 2 + {(- 2)}^{2})}{a (x + 0 - 8)}$

Step 3.2.3.2

Add $x$ and $0$ .

$\frac{(3 - \sqrt[3]{3 (x + 1)}) ({\sqrt[3]{x}}^{2} - \sqrt[3]{x} \cdot - 2 + {(- 2)}^{2})}{a (x - 8)}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

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

$\frac{(3 - \sqrt[3]{3 (x + 1)}) (\sqrt[3]{x^{2}} - \sqrt[3]{x} \cdot - 2 + {(- 2)}^{2})}{a (x - 8)}$

Step 4.2

Multiply $- 2$ by $- 1$ .

$\frac{(3 - \sqrt[3]{3 (x + 1)}) (\sqrt[3]{x^{2}} + 2 \sqrt[3]{x} + {(- 2)}^{2})}{a (x - 8)}$

Step 4.3

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

$\frac{(3 - \sqrt[3]{3 (x + 1)}) (\sqrt[3]{x^{2}} + 2 \sqrt[3]{x} + 4)}{a (x - 8)}$