Pre-Algebra Examples

$\frac{6 x^{9} - 9 x^{8} - 12 x^{6} + 6 x^{4} + 5 x^{3}}{3 x^{6}}$

Step 1

Factor $x^{3}$ out of $6 x^{9} - 9 x^{8} - 12 x^{6} + 6 x^{4} + 5 x^{3}$ .

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Step 1.1

Factor $x^{3}$ out of $6 x^{9}$ .

$\frac{x^{3} (6 x^{6}) - 9 x^{8} - 12 x^{6} + 6 x^{4} + 5 x^{3}}{3 x^{6}}$

Step 1.2

Factor $x^{3}$ out of $- 9 x^{8}$ .

$\frac{x^{3} (6 x^{6}) + x^{3} (- 9 x^{5}) - 12 x^{6} + 6 x^{4} + 5 x^{3}}{3 x^{6}}$

Step 1.3

Factor $x^{3}$ out of $- 12 x^{6}$ .

$\frac{x^{3} (6 x^{6}) + x^{3} (- 9 x^{5}) + x^{3} (- 12 x^{3}) + 6 x^{4} + 5 x^{3}}{3 x^{6}}$

Step 1.4

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

$\frac{x^{3} (6 x^{6}) + x^{3} (- 9 x^{5}) + x^{3} (- 12 x^{3}) + x^{3} (6 x) + 5 x^{3}}{3 x^{6}}$

Step 1.5

Factor $x^{3}$ out of $5 x^{3}$ .

$\frac{x^{3} (6 x^{6}) + x^{3} (- 9 x^{5}) + x^{3} (- 12 x^{3}) + x^{3} (6 x) + x^{3} \cdot 5}{3 x^{6}}$

Step 1.6

Factor $x^{3}$ out of $x^{3} (6 x^{6}) + x^{3} (- 9 x^{5})$ .

$\frac{x^{3} (6 x^{6} - 9 x^{5}) + x^{3} (- 12 x^{3}) + x^{3} (6 x) + x^{3} \cdot 5}{3 x^{6}}$

Step 1.7

Factor $x^{3}$ out of $x^{3} (6 x^{6} - 9 x^{5}) + x^{3} (- 12 x^{3})$ .

$\frac{x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3}) + x^{3} (6 x) + x^{3} \cdot 5}{3 x^{6}}$

Step 1.8

Factor $x^{3}$ out of $x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3}) + x^{3} (6 x)$ .

$\frac{x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x) + x^{3} \cdot 5}{3 x^{6}}$

Step 1.9

Factor $x^{3}$ out of $x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x) + x^{3} \cdot 5$ .

$\frac{x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x + 5)}{3 x^{6}}$

Step 2

Cancel the common factors.

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Step 2.1

Factor $x^{3}$ out of $3 x^{6}$ .

$\frac{x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x + 5)}{x^{3} (3 x^{3})}$

Step 2.2

Cancel the common factor.

$\frac{x^{3} (6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x + 5)}{x^{3} (3 x^{3})}$

Step 2.3

Rewrite the expression.

$\frac{6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x + 5}{3 x^{3}}$

Step 3

Split the fraction $\frac{6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x + 5}{3 x^{3}}$ into two fractions.

$\frac{6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 4

Split the fraction $\frac{6 x^{6} - 9 x^{5} - 12 x^{3} + 6 x}{3 x^{3}}$ into two fractions.

$\frac{6 x^{6} - 9 x^{5} - 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 5

Split the fraction $\frac{6 x^{6} - 9 x^{5} - 12 x^{3}}{3 x^{3}}$ into two fractions.

$\frac{6 x^{6} - 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 6

Split the fraction $\frac{6 x^{6} - 9 x^{5}}{3 x^{3}}$ into two fractions.

$\frac{6 x^{6}}{3 x^{3}} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 7

Cancel the common factor of $6$ and $3$ .

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Step 7.1

Factor $3$ out of $6 x^{6}$ .

$\frac{3 (2 x^{6})}{3 x^{3}} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3 x^{3}$ .

$\frac{3 (2 x^{6})}{3 (x^{3})} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 7.2.2

Cancel the common factor.

$\frac{3 (2 x^{6})}{3 x^{3}} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 7.2.3

Rewrite the expression.

$\frac{2 x^{6}}{x^{3}} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 8

Cancel the common factor of $x^{6}$ and $x^{3}$ .

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Step 8.1

Factor $x^{3}$ out of $2 x^{6}$ .

$\frac{x^{3} (2 x^{3})}{x^{3}} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Multiply by $1$ .

$\frac{x^{3} (2 x^{3})}{x^{3} \cdot 1} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 8.2.2

Cancel the common factor.

$\frac{x^{3} (2 x^{3})}{x^{3} \cdot 1} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 8.2.3

Rewrite the expression.

$\frac{2 x^{3}}{1} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 8.2.4

Divide $2 x^{3}$ by $1$ .

$2 x^{3} + \frac{- 9 x^{5}}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 9

Cancel the common factor of $- 9$ and $3$ .

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Step 9.1

Factor $3$ out of $- 9 x^{5}$ .

$2 x^{3} + \frac{3 (- 3 x^{5})}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $3 x^{3}$ .

$2 x^{3} + \frac{3 (- 3 x^{5})}{3 (x^{3})} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 9.2.2

Cancel the common factor.

$2 x^{3} + \frac{3 (- 3 x^{5})}{3 x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 9.2.3

Rewrite the expression.

$2 x^{3} + \frac{- 3 x^{5}}{x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 10

Cancel the common factor of $x^{5}$ and $x^{3}$ .

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Step 10.1

Factor $x^{3}$ out of $- 3 x^{5}$ .

$2 x^{3} + \frac{x^{3} (- 3 x^{2})}{x^{3}} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Multiply by $1$ .

$2 x^{3} + \frac{x^{3} (- 3 x^{2})}{x^{3} \cdot 1} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 10.2.2

Cancel the common factor.

$2 x^{3} + \frac{x^{3} (- 3 x^{2})}{x^{3} \cdot 1} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 10.2.3

Rewrite the expression.

$2 x^{3} + \frac{- 3 x^{2}}{1} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 10.2.4

Divide $- 3 x^{2}$ by $1$ .

$2 x^{3} - 3 x^{2} + \frac{- 12 x^{3}}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 11

Cancel the common factor of $- 12$ and $3$ .

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Step 11.1

Factor $3$ out of $- 12 x^{3}$ .

$2 x^{3} - 3 x^{2} + \frac{3 (- 4 x^{3})}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $3 x^{3}$ .

$2 x^{3} - 3 x^{2} + \frac{3 (- 4 x^{3})}{3 (x^{3})} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 11.2.2

Cancel the common factor.

$2 x^{3} - 3 x^{2} + \frac{3 (- 4 x^{3})}{3 x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 11.2.3

Rewrite the expression.

$2 x^{3} - 3 x^{2} + \frac{- 4 x^{3}}{x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 12

Cancel the common factor of $x^{3}$ .

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Step 12.1

Cancel the common factor.

$2 x^{3} - 3 x^{2} + \frac{- 4 x^{3}}{x^{3}} + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 12.2

Divide $- 4$ by $1$ .

$2 x^{3} - 3 x^{2} - 4 + \frac{6 x}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 13

Cancel the common factor of $6$ and $3$ .

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Step 13.1

Factor $3$ out of $6 x$ .

$2 x^{3} - 3 x^{2} - 4 + \frac{3 (2 x)}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $3$ out of $3 x^{3}$ .

$2 x^{3} - 3 x^{2} - 4 + \frac{3 (2 x)}{3 (x^{3})} + \frac{5}{3 x^{3}}$

Step 13.2.2

Cancel the common factor.

$2 x^{3} - 3 x^{2} - 4 + \frac{3 (2 x)}{3 x^{3}} + \frac{5}{3 x^{3}}$

Step 13.2.3

Rewrite the expression.

$2 x^{3} - 3 x^{2} - 4 + \frac{2 x}{x^{3}} + \frac{5}{3 x^{3}}$

Step 14

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

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Step 14.1

Factor $x$ out of $2 x$ .

$2 x^{3} - 3 x^{2} - 4 + \frac{x \cdot 2}{x^{3}} + \frac{5}{3 x^{3}}$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Factor $x$ out of $x^{3}$ .

$2 x^{3} - 3 x^{2} - 4 + \frac{x \cdot 2}{x \cdot x^{2}} + \frac{5}{3 x^{3}}$

Step 14.2.2

Cancel the common factor.

$2 x^{3} - 3 x^{2} - 4 + \frac{x \cdot 2}{x \cdot x^{2}} + \frac{5}{3 x^{3}}$

Step 14.2.3

Rewrite the expression.

$2 x^{3} - 3 x^{2} - 4 + \frac{2}{x^{2}} + \frac{5}{3 x^{3}}$