Pre-Algebra Examples

$\frac{2 x - 6}{21} \div \frac{5 x - 15}{12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x - 6}{21} \cdot \frac{12}{5 x - 15}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Factor $3$ out of $21$ .

$\frac{2 x - 6}{3 (7)} \cdot \frac{12}{5 x - 15}$

Step 2.2

Factor $3$ out of $12$ .

$\frac{2 x - 6}{3 \cdot 7} \cdot \frac{3 \cdot 4}{5 x - 15}$

Step 2.3

Cancel the common factor.

$\frac{2 x - 6}{3 \cdot 7} \cdot \frac{3 \cdot 4}{5 x - 15}$

Step 2.4

Rewrite the expression.

$\frac{2 x - 6}{7} \cdot \frac{4}{5 x - 15}$

Step 3

Multiply $\frac{2 x - 6}{7}$ by $\frac{4}{5 x - 15}$ .

$\frac{(2 x - 6) \cdot 4}{7 (5 x - 15)}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $2$ out of $2 x - 6$ .

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Step 4.1.1

Factor $2$ out of $2 x$ .

$\frac{(2 (x) - 6) \cdot 4}{7 (5 x - 15)}$

Step 4.1.2

Factor $2$ out of $- 6$ .

$\frac{(2 x + 2 \cdot - 3) \cdot 4}{7 (5 x - 15)}$

Step 4.1.3

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

$\frac{2 (x - 3) \cdot 4}{7 (5 x - 15)}$

Step 4.2

Multiply $4$ by $2$ .

$\frac{8 (x - 3)}{7 (5 x - 15)}$

Step 5

Simplify the denominator.

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Step 5.1

Factor $5$ out of $5 x - 15$ .

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Step 5.1.1

Factor $5$ out of $5 x$ .

$\frac{8 (x - 3)}{7 (5 (x) - 15)}$

Step 5.1.2

Factor $5$ out of $- 15$ .

$\frac{8 (x - 3)}{7 (5 x + 5 \cdot - 3)}$

Step 5.1.3

Factor $5$ out of $5 x + 5 \cdot - 3$ .

$\frac{8 (x - 3)}{7 (5 (x - 3))}$

$\frac{8 (x - 3)}{7 \cdot 5 (x - 3)}$

Step 5.2

Multiply $7$ by $5$ .

$\frac{8 (x - 3)}{35 (x - 3)}$

Step 6

Cancel the common factor of $x - 3$ .

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Step 6.1

Cancel the common factor.

$\frac{8 (x - 3)}{35 (x - 3)}$

Step 6.2

Rewrite the expression.

$\frac{8}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{35}$

Decimal Form:

$0.2\overline{285714}$