Algebra Examples

$\frac{6 a x}{m^{2} - 2 m} \div \frac{8 a x}{3 m - 6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 a x}{m^{2} - 2 m} \cdot \frac{3 m - 6}{8 a x}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2 a x$ .

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Step 2.1.1

Factor $2 a x$ out of $6 a x$ .

$\frac{2 a x (3)}{m^{2} - 2 m} \cdot \frac{3 m - 6}{8 a x}$

Step 2.1.2

Factor $2 a x$ out of $8 a x$ .

$\frac{2 a x (3)}{m^{2} - 2 m} \cdot \frac{3 m - 6}{2 a x (4)}$

Step 2.1.3

Cancel the common factor.

$\frac{2 a x \cdot 3}{m^{2} - 2 m} \cdot \frac{3 m - 6}{2 a x \cdot 4}$

Step 2.1.4

Rewrite the expression.

$\frac{3}{m^{2} - 2 m} \cdot \frac{3 m - 6}{4}$

Step 2.2

Multiply $\frac{3}{m^{2} - 2 m}$ by $\frac{3 m - 6}{4}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

Factor $3$ out of $3 m - 6$ .

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Step 3.1.1

Factor $3$ out of $3 m$ .

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

Step 3.1.2

Factor $3$ out of $- 6$ .

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

Step 3.1.3

Factor $3$ out of $3 m + 3 \cdot - 2$ .

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

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

Step 3.2

Multiply $3$ by $3$ .

$\frac{9 (m - 2)}{(m^{2} - 2 m) \cdot 4}$

Step 4

Simplify terms.

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Step 4.1

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

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Step 4.1.1

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

$\frac{9 (m - 2)}{(m \cdot m - 2 m) \cdot 4}$

Step 4.1.2

Factor $m$ out of $- 2 m$ .

$\frac{9 (m - 2)}{(m \cdot m + m \cdot - 2) \cdot 4}$

Step 4.1.3

Factor $m$ out of $m \cdot m + m \cdot - 2$ .

$\frac{9 (m - 2)}{m (m - 2) \cdot 4}$

Step 4.2

Cancel the common factor of $m - 2$ .

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Step 4.2.1

Cancel the common factor.

$\frac{9 (m - 2)}{m (m - 2) \cdot 4}$

Step 4.2.2

Rewrite the expression.

$\frac{9}{m \cdot 4}$

Step 4.3

Move $4$ to the left of $m$ .

$\frac{9}{4 m}$