Algebra Examples

$\frac{3 m}{m - 6} \cdot \frac{5 m^{3} - 30 m^{2}}{5 m^{2}}$

Step 1

Factor $5 m^{2}$ out of $5 m^{3} - 30 m^{2}$ .

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Step 1.1

Factor $5 m^{2}$ out of $5 m^{3}$ .

$\frac{3 m}{m - 6} \cdot \frac{5 m^{2} (m) - 30 m^{2}}{5 m^{2}}$

Step 1.2

Factor $5 m^{2}$ out of $- 30 m^{2}$ .

$\frac{3 m}{m - 6} \cdot \frac{5 m^{2} (m) + 5 m^{2} (- 6)}{5 m^{2}}$

Step 1.3

Factor $5 m^{2}$ out of $5 m^{2} (m) + 5 m^{2} (- 6)$ .

$\frac{3 m}{m - 6} \cdot \frac{5 m^{2} (m - 6)}{5 m^{2}}$

Step 2

Cancel the common factor of $m$ .

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Step 2.1

Factor $m$ out of $3 m$ .

$\frac{m \cdot 3}{m - 6} \cdot \frac{5 m^{2} (m - 6)}{5 m^{2}}$

Step 2.2

Factor $m$ out of $5 m^{2}$ .

$\frac{m \cdot 3}{m - 6} \cdot \frac{5 m^{2} (m - 6)}{m (5 m)}$

Step 2.3

Cancel the common factor.

$\frac{m \cdot 3}{m - 6} \cdot \frac{5 m^{2} (m - 6)}{m (5 m)}$

Step 2.4

Rewrite the expression.

$\frac{3}{m - 6} \cdot \frac{5 m^{2} (m - 6)}{5 m}$

Step 3

Cancel the common factor of $m - 6$ .

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Step 3.1

Factor $m - 6$ out of $5 m^{2} (m - 6)$ .

$\frac{3}{m - 6} \cdot \frac{(m - 6) (5 m^{2})}{5 m}$

Step 3.2

Cancel the common factor.

$\frac{3}{m - 6} \cdot \frac{(m - 6) (5 m^{2})}{5 m}$

Step 3.3

Rewrite the expression.

$3 \cdot \frac{5 m^{2}}{5 m}$

Step 4

Combine $3$ and $\frac{5 m^{2}}{5 m}$ .

$\frac{3 (5 m^{2})}{5 m}$

Step 5

Multiply $5$ by $3$ .

$\frac{15 m^{2}}{5 m}$

Step 6

Cancel the common factor of $15$ and $5$ .

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Step 6.1

Factor $5$ out of $15 m^{2}$ .

$\frac{5 (3 m^{2})}{5 m}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 m$ .

$\frac{5 (3 m^{2})}{5 (m)}$

Step 6.2.2

Cancel the common factor.

$\frac{5 (3 m^{2})}{5 m}$

Step 6.2.3

Rewrite the expression.

$\frac{3 m^{2}}{m}$

Step 7

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

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Step 7.1

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

$\frac{m (3 m)}{m}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{m (3 m)}{m^{1}}$

Step 7.2.2

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

$\frac{m (3 m)}{m \cdot 1}$

Step 7.2.3

Cancel the common factor.

$\frac{m (3 m)}{m \cdot 1}$

Step 7.2.4

Rewrite the expression.

$\frac{3 m}{1}$

Step 7.2.5

Divide $3 m$ by $1$ .

$3 m$