Basic Math Examples

$\frac{7 q - 14}{3 q + 6} \cdot \frac{14 q + 28}{6 q - 12}$

Step 1

Factor $7$ out of $7 q - 14$ .

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Step 1.1

Factor $7$ out of $7 q$ .

$\frac{7 (q) - 14}{3 q + 6} \cdot \frac{14 q + 28}{6 q - 12}$

Step 1.2

Factor $7$ out of $- 14$ .

$\frac{7 q + 7 \cdot - 2}{3 q + 6} \cdot \frac{14 q + 28}{6 q - 12}$

Step 1.3

Factor $7$ out of $7 q + 7 \cdot - 2$ .

$\frac{7 (q - 2)}{3 q + 6} \cdot \frac{14 q + 28}{6 q - 12}$

Step 2

Factor $3$ out of $3 q + 6$ .

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Step 2.1

Factor $3$ out of $3 q$ .

$\frac{7 (q - 2)}{3 (q) + 6} \cdot \frac{14 q + 28}{6 q - 12}$

Step 2.2

Factor $3$ out of $6$ .

$\frac{7 (q - 2)}{3 q + 3 \cdot 2} \cdot \frac{14 q + 28}{6 q - 12}$

Step 2.3

Factor $3$ out of $3 q + 3 \cdot 2$ .

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 q + 28}{6 q - 12}$

Step 3

Factor $14$ out of $14 q + 28$ .

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Step 3.1

Factor $14$ out of $14 q$ .

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 (q) + 28}{6 q - 12}$

Step 3.2

Factor $14$ out of $28$ .

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 q + 14 \cdot 2}{6 q - 12}$

Step 3.3

Factor $14$ out of $14 q + 14 \cdot 2$ .

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 (q + 2)}{6 q - 12}$

Step 4

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

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Step 4.1

Factor $6$ out of $6 q$ .

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 (q + 2)}{6 (q) - 12}$

Step 4.2

Factor $6$ out of $- 12$ .

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 (q + 2)}{6 q + 6 \cdot - 2}$

Step 4.3

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

$\frac{7 (q - 2)}{3 (q + 2)} \cdot \frac{14 (q + 2)}{6 (q - 2)}$

Step 5

Cancel the common factor of $q - 2$ .

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Step 5.1

Factor $q - 2$ out of $7 (q - 2)$ .

$\frac{(q - 2) \cdot 7}{3 (q + 2)} \cdot \frac{14 (q + 2)}{6 (q - 2)}$

Step 5.2

Factor $q - 2$ out of $6 (q - 2)$ .

$\frac{(q - 2) \cdot 7}{3 (q + 2)} \cdot \frac{14 (q + 2)}{(q - 2) \cdot 6}$

Step 5.3

Cancel the common factor.

$\frac{(q - 2) \cdot 7}{3 (q + 2)} \cdot \frac{14 (q + 2)}{(q - 2) \cdot 6}$

Step 5.4

Rewrite the expression.

$\frac{7}{3 (q + 2)} \cdot \frac{14 (q + 2)}{6}$

Step 6

Cancel the common factor of $q + 2$ .

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Step 6.1

Factor $q + 2$ out of $3 (q + 2)$ .

$\frac{7}{(q + 2) \cdot 3} \cdot \frac{14 (q + 2)}{6}$

Step 6.2

Factor $q + 2$ out of $14 (q + 2)$ .

$\frac{7}{(q + 2) \cdot 3} \cdot \frac{(q + 2) \cdot 14}{6}$

Step 6.3

Cancel the common factor.

$\frac{7}{(q + 2) \cdot 3} \cdot \frac{(q + 2) \cdot 14}{6}$

Step 6.4

Rewrite the expression.

$\frac{7}{3} \cdot \frac{14}{6}$

Step 7

Multiply $\frac{7}{3}$ by $\frac{14}{6}$ .

$\frac{7 \cdot 14}{3 \cdot 6}$

Step 8

Multiply.

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Step 8.1

Multiply $7$ by $14$ .

$\frac{98}{3 \cdot 6}$

Step 8.2

Multiply $3$ by $6$ .

$\frac{98}{18}$

Step 9

Cancel the common factor of $98$ and $18$ .

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Step 9.1

Factor $2$ out of $98$ .

$\frac{2 (49)}{18}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 49}{2 \cdot 9}$

Step 9.2.2

Cancel the common factor.

$\frac{2 \cdot 49}{2 \cdot 9}$

Step 9.2.3

Rewrite the expression.

$\frac{49}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{9}$

Decimal Form:

$5.\overline{4}$

Mixed Number Form:

$5 \frac{4}{9}$