Algebra Examples

$\frac{\frac{12}{10 x - 40}}{\frac{4}{2 x - 8}}$

Step 1

Cancel the common factor of $12$ and $10 x - 40$ .

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Step 1.1

Factor $2$ out of $12$ .

$\frac{\frac{2 (6)}{10 x - 40}}{\frac{4}{2 x - 8}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $10 x$ .

$\frac{\frac{2 (6)}{2 (5 x) - 40}}{\frac{4}{2 x - 8}}$

Step 1.2.2

Factor $2$ out of $- 40$ .

$\frac{\frac{2 \cdot 6}{2 (5 x) + 2 \cdot - 20}}{\frac{4}{2 x - 8}}$

Step 1.2.3

Factor $2$ out of $2 (5 x) + 2 (- 20)$ .

$\frac{\frac{2 (6)}{2 (5 x - 20)}}{\frac{4}{2 x - 8}}$

Step 1.2.4

Cancel the common factor.

$\frac{\frac{2 \cdot 6}{2 (5 x - 20)}}{\frac{4}{2 x - 8}}$

Step 1.2.5

Rewrite the expression.

$\frac{\frac{6}{5 x - 20}}{\frac{4}{2 x - 8}}$

Step 2

Cancel the common factor of $4$ and $2 x - 8$ .

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Step 2.1

Factor $2$ out of $4$ .

$\frac{\frac{6}{5 x - 20}}{\frac{2 \cdot 2}{2 x - 8}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 x$ .

$\frac{\frac{6}{5 x - 20}}{\frac{2 \cdot 2}{2 (x) - 8}}$

Step 2.2.2

Factor $2$ out of $- 8$ .

$\frac{\frac{6}{5 x - 20}}{\frac{2 \cdot 2}{2 (x) + 2 (- 4)}}$

Step 2.2.3

Factor $2$ out of $2 (x) + 2 (- 4)$ .

$\frac{\frac{6}{5 x - 20}}{\frac{2 \cdot 2}{2 (x - 4)}}$

Step 2.2.4

Cancel the common factor.

$\frac{\frac{6}{5 x - 20}}{\frac{2 \cdot 2}{2 (x - 4)}}$

Step 2.2.5

Rewrite the expression.

$\frac{\frac{6}{5 x - 20}}{\frac{2}{x - 4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{6}{5 x - 20} \cdot \frac{x - 4}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{5 x - 20} \cdot \frac{x - 4}{2}$

Step 4.2

Cancel the common factor.

$\frac{2 \cdot 3}{5 x - 20} \cdot \frac{x - 4}{2}$

Step 4.3

Rewrite the expression.

$\frac{3}{5 x - 20} (x - 4)$

Step 5

Factor $5$ out of $5 x - 20$ .

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Step 5.1

Factor $5$ out of $5 x$ .

$\frac{3}{5 (x) - 20} (x - 4)$

Step 5.2

Factor $5$ out of $- 20$ .

$\frac{3}{5 x + 5 \cdot - 4} (x - 4)$

Step 5.3

Factor $5$ out of $5 x + 5 \cdot - 4$ .

$\frac{3}{5 (x - 4)} (x - 4)$

Step 6

Cancel the common factor of $x - 4$ .

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Step 6.1

Factor $x - 4$ out of $5 (x - 4)$ .

$\frac{3}{(x - 4) \cdot 5} (x - 4)$

Step 6.2

Cancel the common factor.

$\frac{3}{(x - 4) \cdot 5} (x - 4)$

Step 6.3

Rewrite the expression.

$\frac{3}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$