Pre-Algebra Examples

$\frac{\frac{28 x + 14}{45 x - 30}}{\frac{14 x + 7}{30 x - 2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{28 x + 14}{45 x - 30} \cdot \frac{30 x - 2}{14 x + 7}$

Step 2

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

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Step 2.1

Factor $14$ out of $28 x$ .

$\frac{14 (2 x) + 14}{45 x - 30} \cdot \frac{30 x - 2}{14 x + 7}$

Step 2.2

Factor $14$ out of $14$ .

$\frac{14 (2 x) + 14 (1)}{45 x - 30} \cdot \frac{30 x - 2}{14 x + 7}$

Step 2.3

Factor $14$ out of $14 (2 x) + 14 (1)$ .

$\frac{14 (2 x + 1)}{45 x - 30} \cdot \frac{30 x - 2}{14 x + 7}$

Step 3

Factor $15$ out of $45 x - 30$ .

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Step 3.1

Factor $15$ out of $45 x$ .

$\frac{14 (2 x + 1)}{15 (3 x) - 30} \cdot \frac{30 x - 2}{14 x + 7}$

Step 3.2

Factor $15$ out of $- 30$ .

$\frac{14 (2 x + 1)}{15 (3 x) + 15 (- 2)} \cdot \frac{30 x - 2}{14 x + 7}$

Step 3.3

Factor $15$ out of $15 (3 x) + 15 (- 2)$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{30 x - 2}{14 x + 7}$

Step 4

Factor $2$ out of $30 x - 2$ .

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Step 4.1

Factor $2$ out of $30 x$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{2 (15 x) - 2}{14 x + 7}$

Step 4.2

Factor $2$ out of $- 2$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{2 (15 x) + 2 (- 1)}{14 x + 7}$

Step 4.3

Factor $2$ out of $2 (15 x) + 2 (- 1)$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{2 (15 x - 1)}{14 x + 7}$

Step 5

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

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Step 5.1

Factor $7$ out of $14 x$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{2 (15 x - 1)}{7 (2 x) + 7}$

Step 5.2

Factor $7$ out of $7$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{2 (15 x - 1)}{7 (2 x) + 7 (1)}$

Step 5.3

Factor $7$ out of $7 (2 x) + 7 (1)$ .

$\frac{14 (2 x + 1)}{15 (3 x - 2)} \cdot \frac{2 (15 x - 1)}{7 (2 x + 1)}$

Step 6

Cancel the common factor of $7 (2 x + 1)$ .

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Step 6.1

Factor $7 (2 x + 1)$ out of $14 (2 x + 1)$ .

$\frac{7 (2 x + 1) (2)}{15 (3 x - 2)} \cdot \frac{2 (15 x - 1)}{7 (2 x + 1)}$

Step 6.2

Cancel the common factor.

$\frac{7 (2 x + 1) \cdot 2}{15 (3 x - 2)} \cdot \frac{2 (15 x - 1)}{7 (2 x + 1)}$

Step 6.3

Rewrite the expression.

$\frac{2}{15 (3 x - 2)} (2 (15 x - 1))$

Step 7

Combine $2$ and $\frac{2}{15 (3 x - 2)}$ .

$\frac{2 \cdot 2}{15 (3 x - 2)} (15 x - 1)$

Step 8

Multiply $2$ by $2$ .

$\frac{4}{15 (3 x - 2)} (15 x - 1)$

Step 9

Multiply $\frac{4}{15 (3 x - 2)}$ by $15 x - 1$ .

$\frac{4 (15 x - 1)}{15 (3 x - 2)}$