Pre-Algebra Examples

$\frac{12 v^{4} + 6 v^{2} + 18}{2 v}$

Step 1

Cancel the common factor of $12 v^{4} + 6 v^{2} + 18$ and $2$ .

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Step 1.1

Factor $2$ out of $12 v^{4}$ .

$\frac{2 (6 v^{4}) + 6 v^{2} + 18}{2 v}$

Step 1.2

Factor $2$ out of $6 v^{2}$ .

$\frac{2 (6 v^{4}) + 2 (3 v^{2}) + 18}{2 v}$

Step 1.3

Factor $2$ out of $2 (6 v^{4}) + 2 (3 v^{2})$ .

$\frac{2 (6 v^{4} + 3 v^{2}) + 18}{2 v}$

Step 1.4

Factor $2$ out of $18$ .

$\frac{2 (6 v^{4} + 3 v^{2}) + 2 \cdot 9}{2 v}$

Step 1.5

Factor $2$ out of $2 (6 v^{4} + 3 v^{2}) + 2 (9)$ .

$\frac{2 (6 v^{4} + 3 v^{2} + 9)}{2 v}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $2$ out of $2 v$ .

$\frac{2 (6 v^{4} + 3 v^{2} + 9)}{2 (v)}$

Step 1.6.2

Cancel the common factor.

$\frac{2 (6 v^{4} + 3 v^{2} + 9)}{2 v}$

Step 1.6.3

Rewrite the expression.

$\frac{6 v^{4} + 3 v^{2} + 9}{v}$

Step 2

Factor $3$ out of $6 v^{4} + 3 v^{2} + 9$ .

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Step 2.1

Factor $3$ out of $6 v^{4}$ .

$\frac{3 (2 v^{4}) + 3 v^{2} + 9}{v}$

Step 2.2

Factor $3$ out of $3 v^{2}$ .

$\frac{3 (2 v^{4}) + 3 (v^{2}) + 9}{v}$

Step 2.3

Factor $3$ out of $9$ .

$\frac{3 (2 v^{4}) + 3 v^{2} + 3 \cdot 3}{v}$

Step 2.4

Factor $3$ out of $3 (2 v^{4}) + 3 v^{2}$ .

$\frac{3 (2 v^{4} + v^{2}) + 3 \cdot 3}{v}$

Step 2.5

Factor $3$ out of $3 (2 v^{4} + v^{2}) + 3 \cdot 3$ .

$\frac{3 (2 v^{4} + v^{2} + 3)}{v}$

Step 3

Apply the distributive property.

$\frac{3 (2 v^{4}) + 3 v^{2} + 3 \cdot 3}{v}$

Step 4

Simplify.

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Step 4.1

Multiply $2$ by $3$ .

$\frac{6 v^{4} + 3 v^{2} + 3 \cdot 3}{v}$

Step 4.2

Multiply $3$ by $3$ .

$\frac{6 v^{4} + 3 v^{2} + 9}{v}$

Step 5

Split the fraction $\frac{6 v^{4} + 3 v^{2} + 9}{v}$ into two fractions.

$\frac{6 v^{4} + 3 v^{2}}{v} + \frac{9}{v}$

Step 6

Split the fraction $\frac{6 v^{4} + 3 v^{2}}{v}$ into two fractions.

$\frac{6 v^{4}}{v} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 7

Cancel the common factor of $v^{4}$ and $v$ .

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Step 7.1

Factor $v$ out of $6 v^{4}$ .

$\frac{v (6 v^{3})}{v} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Raise $v$ to the power of $1$ .

$\frac{v (6 v^{3})}{v^{1}} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 7.2.2

Factor $v$ out of $v^{1}$ .

$\frac{v (6 v^{3})}{v \cdot 1} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 7.2.3

Cancel the common factor.

$\frac{v (6 v^{3})}{v \cdot 1} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 7.2.4

Rewrite the expression.

$\frac{6 v^{3}}{1} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 7.2.5

Divide $6 v^{3}$ by $1$ .

$6 v^{3} + \frac{3 v^{2}}{v} + \frac{9}{v}$

Step 8

Cancel the common factor of $v^{2}$ and $v$ .

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Step 8.1

Factor $v$ out of $3 v^{2}$ .

$6 v^{3} + \frac{v (3 v)}{v} + \frac{9}{v}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Raise $v$ to the power of $1$ .

$6 v^{3} + \frac{v (3 v)}{v^{1}} + \frac{9}{v}$

Step 8.2.2

Factor $v$ out of $v^{1}$ .

$6 v^{3} + \frac{v (3 v)}{v \cdot 1} + \frac{9}{v}$

Step 8.2.3

Cancel the common factor.

$6 v^{3} + \frac{v (3 v)}{v \cdot 1} + \frac{9}{v}$

Step 8.2.4

Rewrite the expression.

$6 v^{3} + \frac{3 v}{1} + \frac{9}{v}$

Step 8.2.5

Divide $3 v$ by $1$ .

$6 v^{3} + 3 v + \frac{9}{v}$