Pre-Algebra Examples

$\frac{3 x - 9}{7 x + 21} \cdot \frac{6 x + 18}{14 x - 42}$

Step 1

Factor $3$ out of $3 x - 9$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 9}{7 x + 21} \cdot \frac{6 x + 18}{14 x - 42}$

Step 1.2

Factor $3$ out of $- 9$ .

$\frac{3 x + 3 \cdot - 3}{7 x + 21} \cdot \frac{6 x + 18}{14 x - 42}$

Step 1.3

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

$\frac{3 (x - 3)}{7 x + 21} \cdot \frac{6 x + 18}{14 x - 42}$

Step 2

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

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Step 2.1

Factor $7$ out of $7 x$ .

$\frac{3 (x - 3)}{7 (x) + 21} \cdot \frac{6 x + 18}{14 x - 42}$

Step 2.2

Factor $7$ out of $21$ .

$\frac{3 (x - 3)}{7 x + 7 \cdot 3} \cdot \frac{6 x + 18}{14 x - 42}$

Step 2.3

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

$\frac{3 (x - 3)}{7 (x + 3)} \cdot \frac{6 x + 18}{14 x - 42}$

Step 3

Factor $6$ out of $6 x + 18$ .

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Step 3.1

Factor $6$ out of $6 x$ .

$\frac{3 (x - 3)}{7 (x + 3)} \cdot \frac{6 (x) + 18}{14 x - 42}$

Step 3.2

Factor $6$ out of $18$ .

$\frac{3 (x - 3)}{7 (x + 3)} \cdot \frac{6 x + 6 \cdot 3}{14 x - 42}$

Step 3.3

Factor $6$ out of $6 x + 6 \cdot 3$ .

$\frac{3 (x - 3)}{7 (x + 3)} \cdot \frac{6 (x + 3)}{14 x - 42}$

Step 4

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

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Step 4.1

Factor $14$ out of $14 x$ .

$\frac{3 (x - 3)}{7 (x + 3)} \cdot \frac{6 (x + 3)}{14 (x) - 42}$

Step 4.2

Factor $14$ out of $- 42$ .

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

Step 4.3

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

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

Step 5

Cancel the common factor of $x - 3$ .

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

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

Step 6

Cancel the common factor of $x + 3$ .

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Step 6.1

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

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

Step 6.2

Factor $x + 3$ out of $6 (x + 3)$ .

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

Step 6.3

Cancel the common factor.

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

Step 6.4

Rewrite the expression.

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

Step 7

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

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

Step 8

Multiply.

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Step 8.1

Multiply $3$ by $6$ .

$\frac{18}{7 \cdot 14}$

Step 8.2

Multiply $7$ by $14$ .

$\frac{18}{98}$

Step 9

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

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Step 9.1

Factor $2$ out of $18$ .

$\frac{2 (9)}{98}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $98$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

$\frac{9}{49}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{49}$

Decimal Form:

$0.18367346 \dots$