Algebra Examples

$\frac{4}{20 x - 12} \div \frac{1}{20 x^{2} - 12 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{20 x - 12} (20 x^{2} - 12 x)$

Step 2

Cancel the common factor of $4$ and $20 x - 12$ .

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Step 2.1

Factor $4$ out of $4$ .

$\frac{4 (1)}{20 x - 12} (20 x^{2} - 12 x)$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $20 x$ .

$\frac{4 (1)}{4 (5 x) - 12} (20 x^{2} - 12 x)$

Step 2.2.2

Factor $4$ out of $- 12$ .

$\frac{4 \cdot 1}{4 (5 x) + 4 \cdot - 3} (20 x^{2} - 12 x)$

Step 2.2.3

Factor $4$ out of $4 (5 x) + 4 (- 3)$ .

$\frac{4 (1)}{4 (5 x - 3)} (20 x^{2} - 12 x)$

Step 2.2.4

Cancel the common factor.

$\frac{4 \cdot 1}{4 (5 x - 3)} (20 x^{2} - 12 x)$

Step 2.2.5

Rewrite the expression.

$\frac{1}{5 x - 3} (20 x^{2} - 12 x)$

Step 3

Multiply $\frac{1}{5 x - 3}$ by $20 x^{2} - 12 x$ .

$\frac{20 x^{2} - 12 x}{5 x - 3}$

Step 4

Factor $4 x$ out of $20 x^{2} - 12 x$ .

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Step 4.1

Factor $4 x$ out of $20 x^{2}$ .

$\frac{4 x (5 x) - 12 x}{5 x - 3}$

Step 4.2

Factor $4 x$ out of $- 12 x$ .

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

Step 4.3

Factor $4 x$ out of $4 x (5 x) + 4 x (- 3)$ .

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

Step 5

Cancel the common factor of $5 x - 3$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $4 x$ by $1$ .

$4 x$