Pre-Algebra Examples

$\frac{7 x - 21}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 1

Factor $7$ out of $7 x - 21$ .

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Step 1.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) - 21}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 1.2

Factor $7$ out of $- 21$ .

$\frac{7 x + 7 \cdot - 3}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 1.3

Factor $7$ out of $7 x + 7 \cdot - 3$ .

$\frac{7 (x - 3)}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 2

Factor $5$ out of $5 x + 15$ .

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Step 2.1

Factor $5$ out of $5 x$ .

$\frac{7 (x - 3)}{5 (x) + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 2.2

Factor $5$ out of $15$ .

$\frac{7 (x - 3)}{5 x + 5 \cdot 3} \cdot \frac{14 x + 42}{10 x - 30}$

Step 2.3

Factor $5$ out of $5 x + 5 \cdot 3$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 x + 42}{10 x - 30}$

Step 3

Factor $14$ out of $14 x + 42$ .

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Step 3.1

Factor $14$ out of $14 x$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x) + 42}{10 x - 30}$

Step 3.2

Factor $14$ out of $42$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 x + 14 \cdot 3}{10 x - 30}$

Step 3.3

Factor $14$ out of $14 x + 14 \cdot 3$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 x - 30}$

Step 4

Factor $10$ out of $10 x - 30$ .

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Step 4.1

Factor $10$ out of $10 x$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 (x) - 30}$

Step 4.2

Factor $10$ out of $- 30$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 x + 10 \cdot - 3}$

Step 4.3

Factor $10$ out of $10 x + 10 \cdot - 3$ .

$\frac{7 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 (x - 3)}$

Step 5

Cancel the common factor of $x - 3$ .

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Step 5.1

Factor $x - 3$ out of $7 (x - 3)$ .

$\frac{(x - 3) \cdot 7}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 (x - 3)}$

Step 5.2

Factor $x - 3$ out of $10 (x - 3)$ .

$\frac{(x - 3) \cdot 7}{5 (x + 3)} \cdot \frac{14 (x + 3)}{(x - 3) \cdot 10}$

Step 5.3

Cancel the common factor.

$\frac{(x - 3) \cdot 7}{5 (x + 3)} \cdot \frac{14 (x + 3)}{(x - 3) \cdot 10}$

Step 5.4

Rewrite the expression.

$\frac{7}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10}$

Step 6

Cancel the common factor of $x + 3$ .

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Step 6.1

Factor $x + 3$ out of $5 (x + 3)$ .

$\frac{7}{(x + 3) \cdot 5} \cdot \frac{14 (x + 3)}{10}$

Step 6.2

Factor $x + 3$ out of $14 (x + 3)$ .

$\frac{7}{(x + 3) \cdot 5} \cdot \frac{(x + 3) \cdot 14}{10}$

Step 6.3

Cancel the common factor.

$\frac{7}{(x + 3) \cdot 5} \cdot \frac{(x + 3) \cdot 14}{10}$

Step 6.4

Rewrite the expression.

$\frac{7}{5} \cdot \frac{14}{10}$

Step 7

Multiply $\frac{7}{5}$ by $\frac{14}{10}$ .

$\frac{7 \cdot 14}{5 \cdot 10}$

Step 8

Multiply.

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Step 8.1

Multiply $7$ by $14$ .

$\frac{98}{5 \cdot 10}$

Step 8.2

Multiply $5$ by $10$ .

$\frac{98}{50}$

Step 9

Cancel the common factor of $98$ and $50$ .

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Step 9.1

Factor $2$ out of $98$ .

$\frac{2 (49)}{50}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $50$ .

$\frac{2 \cdot 49}{2 \cdot 25}$

Step 9.2.2

Cancel the common factor.

$\frac{2 \cdot 49}{2 \cdot 25}$

Step 9.2.3

Rewrite the expression.

$\frac{49}{25}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{25}$

Decimal Form:

$1.96$

Mixed Number Form:

$1 \frac{24}{25}$