Algebra Examples

$\frac{12 m^{4} - 24 m^{3} + 6 m^{2} + 9 m - 9}{6 m^{2}}$

Step 1

Cancel the common factor of $12 m^{4} - 24 m^{3} + 6 m^{2} + 9 m - 9$ and $6$ .

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Step 1.1

Factor $3$ out of $12 m^{4}$ .

$\frac{3 (4 m^{4}) - 24 m^{3} + 6 m^{2} + 9 m - 9}{6 m^{2}}$

Step 1.2

Factor $3$ out of $- 24 m^{3}$ .

$\frac{3 (4 m^{4}) + 3 (- 8 m^{3}) + 6 m^{2} + 9 m - 9}{6 m^{2}}$

Step 1.3

Factor $3$ out of $3 (4 m^{4}) + 3 (- 8 m^{3})$ .

$\frac{3 (4 m^{4} - 8 m^{3}) + 6 m^{2} + 9 m - 9}{6 m^{2}}$

Step 1.4

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

$\frac{3 (4 m^{4} - 8 m^{3}) + 3 (2 m^{2}) + 9 m - 9}{6 m^{2}}$

Step 1.5

Factor $3$ out of $3 (4 m^{4} - 8 m^{3}) + 3 (2 m^{2})$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2}) + 9 m - 9}{6 m^{2}}$

Step 1.6

Factor $3$ out of $9 m$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2}) + 3 (3 m) - 9}{6 m^{2}}$

Step 1.7

Factor $3$ out of $3 (4 m^{4} - 8 m^{3} + 2 m^{2}) + 3 (3 m)$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m) - 9}{6 m^{2}}$

Step 1.8

Factor $3$ out of $- 9$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m) + 3 (- 3)}{6 m^{2}}$

Step 1.9

Factor $3$ out of $3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m) + 3 (- 3)$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m - 3)}{6 m^{2}}$

Step 1.10

Cancel the common factors.

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Step 1.10.1

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

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m - 3)}{3 (2 m^{2})}$

Step 1.10.2

Cancel the common factor.

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m - 3)}{3 (2 m^{2})}$

Step 1.10.3

Rewrite the expression.

$\frac{4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m - 3}{2 m^{2}}$

Step 2

Split the fraction $\frac{4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m - 3}{2 m^{2}}$ into two fractions.

$\frac{4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 3

Split the fraction $\frac{4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m}{2 m^{2}}$ into two fractions.

$\frac{4 m^{4} - 8 m^{3} + 2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 4

Split the fraction $\frac{4 m^{4} - 8 m^{3} + 2 m^{2}}{2 m^{2}}$ into two fractions.

$\frac{4 m^{4} - 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 5

Split the fraction $\frac{4 m^{4} - 8 m^{3}}{2 m^{2}}$ into two fractions.

$\frac{4 m^{4}}{2 m^{2}} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 6

Cancel the common factor of $4$ and $2$ .

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Step 6.1

Factor $2$ out of $4 m^{4}$ .

$\frac{2 (2 m^{4})}{2 m^{2}} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 m^{2}$ .

$\frac{2 (2 m^{4})}{2 (m^{2})} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (2 m^{4})}{2 m^{2}} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 6.2.3

Rewrite the expression.

$\frac{2 m^{4}}{m^{2}} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 7

Cancel the common factor of $m^{4}$ and $m^{2}$ .

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Step 7.1

Factor $m^{2}$ out of $2 m^{4}$ .

$\frac{m^{2} (2 m^{2})}{m^{2}} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Multiply by $1$ .

$\frac{m^{2} (2 m^{2})}{m^{2} \cdot 1} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 7.2.2

Cancel the common factor.

$\frac{m^{2} (2 m^{2})}{m^{2} \cdot 1} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 7.2.3

Rewrite the expression.

$\frac{2 m^{2}}{1} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 7.2.4

Divide $2 m^{2}$ by $1$ .

$2 m^{2} + \frac{- 8 m^{3}}{2 m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 8

Cancel the common factor of $- 8$ and $2$ .

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Step 8.1

Factor $2$ out of $- 8 m^{3}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2 m^{2}$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$2 m^{2} + \frac{- 4 m^{3}}{m^{2}} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 9

Cancel the common factor of $m^{3}$ and $m^{2}$ .

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Step 9.1

Factor $m^{2}$ out of $- 4 m^{3}$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

$2 m^{2} + \frac{- 4 m}{1} + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 9.2.4

Divide $- 4 m$ by $1$ .

$2 m^{2} - 4 m + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 10

Cancel the common factor of $2$ .

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Step 10.1

Cancel the common factor.

$2 m^{2} - 4 m + \frac{2 m^{2}}{2 m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 10.2

Rewrite the expression.

$2 m^{2} - 4 m + \frac{m^{2}}{m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 11

Cancel the common factor of $m^{2}$ .

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Step 11.1

Cancel the common factor.

$2 m^{2} - 4 m + \frac{m^{2}}{m^{2}} + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 11.2

Rewrite the expression.

$2 m^{2} - 4 m + 1 + \frac{3 m}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 12

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

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Step 12.1

Factor $m$ out of $3 m$ .

$2 m^{2} - 4 m + 1 + \frac{m \cdot 3}{2 m^{2}} + \frac{- 3}{2 m^{2}}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $m$ out of $2 m^{2}$ .

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

Step 12.2.2

Cancel the common factor.

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

Step 12.2.3

Rewrite the expression.

$2 m^{2} - 4 m + 1 + \frac{3}{2 m} + \frac{- 3}{2 m^{2}}$

Step 13

Move the negative in front of the fraction.

$2 m^{2} - 4 m + 1 + \frac{3}{2 m} - \frac{3}{2 m^{2}}$