Finite Math Examples

$(\frac{3 x - 6}{7 x + 14}) (\frac{10 x + 20}{14 x - 28})$

Step 1

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

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{7 x + 14} \cdot \frac{10 x + 20}{14 x - 28}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{7 x + 14} \cdot \frac{10 x + 20}{14 x - 28}$

Step 1.3

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

$\frac{3 (x - 2)}{7 x + 14} \cdot \frac{10 x + 20}{14 x - 28}$

Step 2

Factor $7$ out of $7 x + 14$ .

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Step 2.1

Factor $7$ out of $7 x$ .

$\frac{3 (x - 2)}{7 (x) + 14} \cdot \frac{10 x + 20}{14 x - 28}$

Step 2.2

Factor $7$ out of $14$ .

$\frac{3 (x - 2)}{7 x + 7 \cdot 2} \cdot \frac{10 x + 20}{14 x - 28}$

Step 2.3

Factor $7$ out of $7 x + 7 \cdot 2$ .

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 x + 20}{14 x - 28}$

Step 3

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

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Step 3.1

Factor $10$ out of $10 x$ .

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 (x) + 20}{14 x - 28}$

Step 3.2

Factor $10$ out of $20$ .

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 x + 10 \cdot 2}{14 x - 28}$

Step 3.3

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

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 (x + 2)}{14 x - 28}$

Step 4

Factor $14$ out of $14 x - 28$ .

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Step 4.1

Factor $14$ out of $14 x$ .

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 (x + 2)}{14 (x) - 28}$

Step 4.2

Factor $14$ out of $- 28$ .

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 (x + 2)}{14 x + 14 \cdot - 2}$

Step 4.3

Factor $14$ out of $14 x + 14 \cdot - 2$ .

$\frac{3 (x - 2)}{7 (x + 2)} \cdot \frac{10 (x + 2)}{14 (x - 2)}$

Step 5

Cancel the common factor of $x - 2$ .

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Step 5.1

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

$\frac{(x - 2) \cdot 3}{7 (x + 2)} \cdot \frac{10 (x + 2)}{14 (x - 2)}$

Step 5.2

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

$\frac{(x - 2) \cdot 3}{7 (x + 2)} \cdot \frac{10 (x + 2)}{(x - 2) \cdot 14}$

Step 5.3

Cancel the common factor.

$\frac{(x - 2) \cdot 3}{7 (x + 2)} \cdot \frac{10 (x + 2)}{(x - 2) \cdot 14}$

Step 5.4

Rewrite the expression.

$\frac{3}{7 (x + 2)} \cdot \frac{10 (x + 2)}{14}$

Step 6

Cancel the common factor of $x + 2$ .

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Step 6.1

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

$\frac{3}{(x + 2) \cdot 7} \cdot \frac{10 (x + 2)}{14}$

Step 6.2

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

$\frac{3}{(x + 2) \cdot 7} \cdot \frac{(x + 2) \cdot 10}{14}$

Step 6.3

Cancel the common factor.

$\frac{3}{(x + 2) \cdot 7} \cdot \frac{(x + 2) \cdot 10}{14}$

Step 6.4

Rewrite the expression.

$\frac{3}{7} \cdot \frac{10}{14}$

Step 7

Multiply $\frac{3}{7}$ by $\frac{10}{14}$ .

$\frac{3 \cdot 10}{7 \cdot 14}$

Step 8

Multiply.

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Step 8.1

Multiply $3$ by $10$ .

$\frac{30}{7 \cdot 14}$

Step 8.2

Multiply $7$ by $14$ .

$\frac{30}{98}$

Step 9

Cancel the common factor of $30$ and $98$ .

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Step 9.1

Factor $2$ out of $30$ .

$\frac{2 (15)}{98}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $98$ .

$\frac{2 \cdot 15}{2 \cdot 49}$

Step 9.2.2

Cancel the common factor.

$\frac{2 \cdot 15}{2 \cdot 49}$

Step 9.2.3

Rewrite the expression.

$\frac{15}{49}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{49}$

Decimal Form:

$0.30612244 \dots$