Pre-Algebra Examples

$\frac{6 a^{4} - 2 a^{3} + 2}{2 a}$

Step 1

Cancel the common factor of $6 a^{4} - 2 a^{3} + 2$ and $2$ .

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Step 1.1

Factor $2$ out of $6 a^{4}$ .

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

Step 1.2

Factor $2$ out of $- 2 a^{3}$ .

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

Step 1.3

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

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

Step 1.4

Factor $2$ out of $2$ .

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

Step 1.5

Factor $2$ out of $2 (3 a^{4} - a^{3}) + 2 (1)$ .

$\frac{2 (3 a^{4} - a^{3} + 1)}{2 a}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $2$ out of $2 a$ .

$\frac{2 (3 a^{4} - a^{3} + 1)}{2 (a)}$

Step 1.6.2

Cancel the common factor.

$\frac{2 (3 a^{4} - a^{3} + 1)}{2 a}$

Step 1.6.3

Rewrite the expression.

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

Step 2

Split the fraction $\frac{3 a^{4} - a^{3} + 1}{a}$ into two fractions.

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

Step 3

Split the fraction $\frac{3 a^{4} - a^{3}}{a}$ into two fractions.

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

Step 4

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

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Step 4.1

Factor $a$ out of $3 a^{4}$ .

$\frac{a (3 a^{3})}{a} + \frac{- a^{3}}{a} + \frac{1}{a}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{a (3 a^{3})}{a^{1}} + \frac{- a^{3}}{a} + \frac{1}{a}$

Step 4.2.2

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

$\frac{a (3 a^{3})}{a \cdot 1} + \frac{- a^{3}}{a} + \frac{1}{a}$

Step 4.2.3

Cancel the common factor.

$\frac{a (3 a^{3})}{a \cdot 1} + \frac{- a^{3}}{a} + \frac{1}{a}$

Step 4.2.4

Rewrite the expression.

$\frac{3 a^{3}}{1} + \frac{- a^{3}}{a} + \frac{1}{a}$

Step 4.2.5

Divide $3 a^{3}$ by $1$ .

$3 a^{3} + \frac{- a^{3}}{a} + \frac{1}{a}$

Step 5

Cancel the common factor of $a^{3}$ and $a$ .

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Step 5.1

Factor $a$ out of $- a^{3}$ .

$3 a^{3} + \frac{a (- a^{2})}{a} + \frac{1}{a}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$3 a^{3} + \frac{a (- a^{2})}{a^{1}} + \frac{1}{a}$

Step 5.2.2

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

$3 a^{3} + \frac{a (- a^{2})}{a \cdot 1} + \frac{1}{a}$

Step 5.2.3

Cancel the common factor.

$3 a^{3} + \frac{a (- a^{2})}{a \cdot 1} + \frac{1}{a}$

Step 5.2.4

Rewrite the expression.

$3 a^{3} + \frac{- a^{2}}{1} + \frac{1}{a}$

Step 5.2.5

Divide $- a^{2}$ by $1$ .

$3 a^{3} - a^{2} + \frac{1}{a}$