Algebra Examples

$\frac{12 - 14 x}{4} \cdot \frac{6 x + 8}{30 - 35 x}$

Step 1

Factor $2$ out of $12 - 14 x$ .

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Step 1.1

Factor $2$ out of $12$ .

$\frac{2 (6) - 14 x}{4} \cdot \frac{6 x + 8}{30 - 35 x}$

Step 1.2

Factor $2$ out of $- 14 x$ .

$\frac{2 (6) + 2 (- 7 x)}{4} \cdot \frac{6 x + 8}{30 - 35 x}$

Step 1.3

Factor $2$ out of $2 (6) + 2 (- 7 x)$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{6 x + 8}{30 - 35 x}$

Step 2

Factor $2$ out of $6 x + 8$ .

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Step 2.1

Factor $2$ out of $6 x$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{2 (3 x) + 8}{30 - 35 x}$

Step 2.2

Factor $2$ out of $8$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{2 (3 x) + 2 (4)}{30 - 35 x}$

Step 2.3

Factor $2$ out of $2 (3 x) + 2 (4)$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{2 (3 x + 4)}{30 - 35 x}$

Step 3

Factor $5$ out of $30 - 35 x$ .

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Step 3.1

Factor $5$ out of $30$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{2 (3 x + 4)}{5 (6) - 35 x}$

Step 3.2

Factor $5$ out of $- 35 x$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{2 (3 x + 4)}{5 (6) + 5 (- 7 x)}$

Step 3.3

Factor $5$ out of $5 (6) + 5 (- 7 x)$ .

$\frac{2 (6 - 7 x)}{4} \cdot \frac{2 (3 x + 4)}{5 (6 - 7 x)}$

Step 4

Cancel the common factor of $6 - 7 x$ .

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Step 4.1

Factor $6 - 7 x$ out of $2 (6 - 7 x)$ .

$\frac{(6 - 7 x) \cdot 2}{4} \cdot \frac{2 (3 x + 4)}{5 (6 - 7 x)}$

Step 4.2

Factor $6 - 7 x$ out of $5 (6 - 7 x)$ .

$\frac{(6 - 7 x) \cdot 2}{4} \cdot \frac{2 (3 x + 4)}{(6 - 7 x) \cdot 5}$

Step 4.3

Cancel the common factor.

$\frac{(6 - 7 x) \cdot 2}{4} \cdot \frac{2 (3 x + 4)}{(6 - 7 x) \cdot 5}$

Step 4.4

Rewrite the expression.

$\frac{2}{4} \cdot \frac{2 (3 x + 4)}{5}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $4$ .

$\frac{2}{2 (2)} \cdot \frac{2 (3 x + 4)}{5}$

Step 5.2

Cancel the common factor.

$\frac{2}{2 \cdot 2} \cdot \frac{2 (3 x + 4)}{5}$

Step 5.3

Rewrite the expression.

$\frac{2}{2} \cdot \frac{3 x + 4}{5}$

Step 6

Multiply $\frac{2}{2}$ by $\frac{3 x + 4}{5}$ .

$\frac{2 (3 x + 4)}{2 \cdot 5}$

Step 7

Multiply $2$ by $5$ .

$\frac{2 (3 x + 4)}{10}$

Step 8

Cancel the common factors.

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Step 8.1

Factor $2$ out of $10$ .

$\frac{2 (3 x + 4)}{2 \cdot 5}$

Step 8.2

Cancel the common factor.

$\frac{2 (3 x + 4)}{2 \cdot 5}$

Step 8.3

Rewrite the expression.

$\frac{3 x + 4}{5}$