Algebra Examples

$\frac{6 x - 12}{4 x^{2}} \cdot \frac{3 x^{3}}{2 x - 4}$

Step 1

Simplify terms.

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Step 1.1

Factor $6$ out of $6 x - 12$ .

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Step 1.1.1

Factor $6$ out of $6 x$ .

$\frac{6 (x) - 12}{4 x^{2}} \cdot \frac{3 x^{3}}{2 x - 4}$

Step 1.1.2

Factor $6$ out of $- 12$ .

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

Step 1.1.3

Factor $6$ out of $6 x + 6 \cdot - 2$ .

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

Step 1.2

Factor $2$ out of $2 x - 4$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

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

Step 1.2.2

Factor $2$ out of $- 4$ .

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

Step 1.2.3

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

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

Step 1.3

Combine.

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

Step 1.4

Cancel the common factor of $6$ and $4$ .

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Step 1.4.1

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

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

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $2$ out of $4 x^{2} (2 (x - 2))$ .

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

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

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

Step 1.5

Cancel the common factor of $x - 2$ .

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Step 1.5.1

Cancel the common factor.

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

Step 1.5.2

Rewrite the expression.

$\frac{3 (3 x^{3})}{2 x^{2} \cdot (2)}$

Step 1.6

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

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Step 1.6.1

Factor $x^{2}$ out of $3 (3 x^{3})$ .

$\frac{x^{2} (3 (3 x))}{2 x^{2} \cdot (2)}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $x^{2}$ out of $2 x^{2} \cdot (2)$ .

$\frac{x^{2} (3 (3 x))}{x^{2} (2 \cdot (2))}$

Step 1.6.2.2

Cancel the common factor.

$\frac{x^{2} (3 (3 x))}{x^{2} (2 \cdot (2))}$

Step 1.6.2.3

Rewrite the expression.

$\frac{3 (3 x)}{2 \cdot (2)}$

Step 1.7

Multiply $3$ by $3$ .

$\frac{9 x}{2 \cdot (2)}$

Step 2

Multiply $2$ by $2$ .

$\frac{9 x}{4}$