Algebra Examples

$\frac{6 k^{2} m - 12 k^{3} m^{2} + 9 m^{3}}{2 (k m^{2})}$

Step 1

Factor $3 m$ out of $6 k^{2} m - 12 k^{3} m^{2} + 9 m^{3}$ .

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Step 1.1

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

$\frac{3 m (2 k^{2}) - 12 k^{3} m^{2} + 9 m^{3}}{2 k m^{2}}$

Step 1.2

Factor $3 m$ out of $- 12 k^{3} m^{2}$ .

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

Step 1.3

Factor $3 m$ out of $9 m^{3}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Apply the distributive property.

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

Step 4

Simplify.

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Step 4.1

Multiply $2$ by $3$ .

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

Step 4.2

Multiply $- 4$ by $3$ .

$\frac{6 k^{2} - 12 (k^{3} m) + 3 (3 m^{2})}{2 k m}$

Step 4.3

Multiply $3$ by $3$ .

$\frac{6 k^{2} - 12 (k^{3} m) + 9 m^{2}}{2 k m}$

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

Step 5

Split the fraction $\frac{6 k^{2} - 12 k^{3} m + 9 m^{2}}{2 k m}$ into two fractions.

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

Step 6

Split the fraction $\frac{6 k^{2} - 12 k^{3} m}{2 k m}$ into two fractions.

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

Step 7

Cancel the common factor of $6$ and $2$ .

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Step 7.1

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

$\frac{2 (3 k^{2})}{2 k m} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2 k m$ .

$\frac{2 (3 k^{2})}{2 (k m)} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (3 k^{2})}{2 (k m)} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 7.2.3

Rewrite the expression.

$\frac{3 k^{2}}{k m} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 8

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

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Step 8.1

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

$\frac{k (3 k)}{k m} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $k$ out of $k m$ .

$\frac{k (3 k)}{k (m)} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 8.2.2

Cancel the common factor.

$\frac{k (3 k)}{k m} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 8.2.3

Rewrite the expression.

$\frac{3 k}{m} + \frac{- 12 k^{3} m}{2 k m} + \frac{9 m^{2}}{2 k m}$

Step 9

Cancel the common factor of $- 12$ and $2$ .

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Step 9.1

Factor $2$ out of $- 12 k^{3} m$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $2 k m$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

$\frac{3 k}{m} + \frac{- 6 k^{3} m}{k m} + \frac{9 m^{2}}{2 k m}$

Step 10

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

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Step 10.1

Factor $k$ out of $- 6 k^{3} m$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $k$ out of $k m$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

$\frac{3 k}{m} + \frac{- 6 k^{2} m}{m} + \frac{9 m^{2}}{2 k m}$

Step 11

Cancel the common factor of $m$ .

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Step 11.1

Cancel the common factor.

$\frac{3 k}{m} + \frac{- 6 k^{2} m}{m} + \frac{9 m^{2}}{2 k m}$

Step 11.2

Divide $- 6 k^{2}$ by $1$ .

$\frac{3 k}{m} - 6 k^{2} + \frac{9 m^{2}}{2 k m}$

Step 12

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

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Step 12.1

Factor $m$ out of $9 m^{2}$ .

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

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $m$ out of $2 k m$ .

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

Step 12.2.2

Cancel the common factor.

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

Step 12.2.3

Rewrite the expression.

$\frac{3 k}{m} - 6 k^{2} + \frac{9 m}{2 k}$