Pre-Algebra Examples

$\frac{5 (x + 6)}{10 (x - 6)} \div \frac{20 (x + 6)}{8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 (x + 6)}{10 (x - 6)} \cdot \frac{8}{20 (x + 6)}$

Step 2

Cancel the common factor of $5 (x + 6)$ .

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Step 2.1

Factor $5 (x + 6)$ out of $20 (x + 6)$ .

$\frac{5 (x + 6)}{10 (x - 6)} \cdot \frac{8}{5 (x + 6) (4)}$

Step 2.2

Cancel the common factor.

$\frac{5 (x + 6)}{10 (x - 6)} \cdot \frac{8}{5 (x + 6) \cdot 4}$

Step 2.3

Rewrite the expression.

$\frac{1}{10 (x - 6)} \cdot \frac{8}{4}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $10 (x - 6)$ .

$\frac{1}{2 (5 (x - 6))} \cdot \frac{8}{4}$

Step 3.2

Factor $2$ out of $8$ .

$\frac{1}{2 (5 (x - 6))} \cdot \frac{2 (4)}{4}$

Step 3.3

Cancel the common factor.

$\frac{1}{2 (5 (x - 6))} \cdot \frac{2 \cdot 4}{4}$

Step 3.4

Rewrite the expression.

$\frac{1}{5 (x - 6)} \cdot \frac{4}{4}$

Step 4

Multiply $\frac{1}{5 (x - 6)}$ by $\frac{4}{4}$ .

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

Step 5

Multiply $4$ by $5$ .

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

Step 6

Cancel the common factor of $4$ and $20$ .

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Step 6.1

Factor $4$ out of $4$ .

$\frac{4 (1)}{20 (x - 6)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $20 (x - 6)$ .

$\frac{4 (1)}{4 (5 (x - 6))}$

Step 6.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 (5 (x - 6))}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{5 (x - 6)}$