Pre-Algebra Examples

$\frac{x - 7}{3 x + 12} \div \frac{2 x - 14}{9 x + 36}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 7}{3 x + 12} \cdot \frac{9 x + 36}{2 x - 14}$

Step 2

Factor $3$ out of $3 x + 12$ .

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{x - 7}{3 (x) + 12} \cdot \frac{9 x + 36}{2 x - 14}$

Step 2.2

Factor $3$ out of $12$ .

$\frac{x - 7}{3 x + 3 \cdot 4} \cdot \frac{9 x + 36}{2 x - 14}$

Step 2.3

Factor $3$ out of $3 x + 3 \cdot 4$ .

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 x + 36}{2 x - 14}$

Step 3

Factor $9$ out of $9 x + 36$ .

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Step 3.1

Factor $9$ out of $9 x$ .

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x) + 36}{2 x - 14}$

Step 3.2

Factor $9$ out of $36$ .

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 x + 9 \cdot 4}{2 x - 14}$

Step 3.3

Factor $9$ out of $9 x + 9 \cdot 4$ .

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x + 4)}{2 x - 14}$

Step 4

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

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Step 4.1

Factor $2$ out of $2 x$ .

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x + 4)}{2 (x) - 14}$

Step 4.2

Factor $2$ out of $- 14$ .

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x + 4)}{2 x + 2 \cdot - 7}$

Step 4.3

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

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x + 4)}{2 (x - 7)}$

Step 5

Cancel the common factor of $x - 7$ .

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Step 5.1

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

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x + 4)}{(x - 7) \cdot 2}$

Step 5.2

Cancel the common factor.

$\frac{x - 7}{3 (x + 4)} \cdot \frac{9 (x + 4)}{(x - 7) \cdot 2}$

Step 5.3

Rewrite the expression.

$\frac{1}{3 (x + 4)} \cdot \frac{9 (x + 4)}{2}$

Step 6

Cancel the common factor of $3 (x + 4)$ .

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Step 6.1

Factor $3 (x + 4)$ out of $9 (x + 4)$ .

$\frac{1}{3 (x + 4)} \cdot \frac{3 (x + 4) (3)}{2}$

Step 6.2

Cancel the common factor.

$\frac{1}{3 (x + 4)} \cdot \frac{3 (x + 4) \cdot 3}{2}$

Step 6.3

Rewrite the expression.

$\frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$