Finite Math Examples

$\frac{3 x - 6}{5 x + 10} \cdot \frac{6 x + 12}{10 x - 20}$

Step 1

Factor $3$ out of $3 x - 6$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{5 x + 10} \cdot \frac{6 x + 12}{10 x - 20}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{5 x + 10} \cdot \frac{6 x + 12}{10 x - 20}$

Step 1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{5 x + 10} \cdot \frac{6 x + 12}{10 x - 20}$

Step 2

Factor $5$ out of $5 x + 10$ .

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Step 2.1

Factor $5$ out of $5 x$ .

$\frac{3 (x - 2)}{5 (x) + 10} \cdot \frac{6 x + 12}{10 x - 20}$

Step 2.2

Factor $5$ out of $10$ .

$\frac{3 (x - 2)}{5 x + 5 \cdot 2} \cdot \frac{6 x + 12}{10 x - 20}$

Step 2.3

Factor $5$ out of $5 x + 5 \cdot 2$ .

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 x + 12}{10 x - 20}$

Step 3

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

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Step 3.1

Factor $6$ out of $6 x$ .

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 (x) + 12}{10 x - 20}$

Step 3.2

Factor $6$ out of $12$ .

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 x + 6 \cdot 2}{10 x - 20}$

Step 3.3

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

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 (x + 2)}{10 x - 20}$

Step 4

Factor $10$ out of $10 x - 20$ .

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Step 4.1

Factor $10$ out of $10 x$ .

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 (x + 2)}{10 (x) - 20}$

Step 4.2

Factor $10$ out of $- 20$ .

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 (x + 2)}{10 x + 10 \cdot - 2}$

Step 4.3

Factor $10$ out of $10 x + 10 \cdot - 2$ .

$\frac{3 (x - 2)}{5 (x + 2)} \cdot \frac{6 (x + 2)}{10 (x - 2)}$

Step 5

Cancel the common factor of $x - 2$ .

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Step 5.1

Factor $x - 2$ out of $3 (x - 2)$ .

$\frac{(x - 2) \cdot 3}{5 (x + 2)} \cdot \frac{6 (x + 2)}{10 (x - 2)}$

Step 5.2

Factor $x - 2$ out of $10 (x - 2)$ .

$\frac{(x - 2) \cdot 3}{5 (x + 2)} \cdot \frac{6 (x + 2)}{(x - 2) \cdot 10}$

Step 5.3

Cancel the common factor.

$\frac{(x - 2) \cdot 3}{5 (x + 2)} \cdot \frac{6 (x + 2)}{(x - 2) \cdot 10}$

Step 5.4

Rewrite the expression.

$\frac{3}{5 (x + 2)} \cdot \frac{6 (x + 2)}{10}$

Step 6

Cancel the common factor of $x + 2$ .

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Step 6.1

Factor $x + 2$ out of $5 (x + 2)$ .

$\frac{3}{(x + 2) \cdot 5} \cdot \frac{6 (x + 2)}{10}$

Step 6.2

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

$\frac{3}{(x + 2) \cdot 5} \cdot \frac{(x + 2) \cdot 6}{10}$

Step 6.3

Cancel the common factor.

$\frac{3}{(x + 2) \cdot 5} \cdot \frac{(x + 2) \cdot 6}{10}$

Step 6.4

Rewrite the expression.

$\frac{3}{5} \cdot \frac{6}{10}$

Step 7

Multiply $\frac{3}{5}$ by $\frac{6}{10}$ .

$\frac{3 \cdot 6}{5 \cdot 10}$

Step 8

Multiply.

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Step 8.1

Multiply $3$ by $6$ .

$\frac{18}{5 \cdot 10}$

Step 8.2

Multiply $5$ by $10$ .

$\frac{18}{50}$

Step 9

Cancel the common factor of $18$ and $50$ .

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Step 9.1

Factor $2$ out of $18$ .

$\frac{2 (9)}{50}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $50$ .

$\frac{2 \cdot 9}{2 \cdot 25}$

Step 9.2.2

Cancel the common factor.

$\frac{2 \cdot 9}{2 \cdot 25}$

Step 9.2.3

Rewrite the expression.

$\frac{9}{25}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{25}$

Decimal Form:

$0.36$