Algebra Examples

$\frac{x}{2 x - 8} \div \frac{5}{3 x - 12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x}{2 x - 8} \cdot \frac{3 x - 12}{5}$

Step 2

Factor $2$ out of $2 x - 8$ .

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Step 2.1

Factor $2$ out of $2 x$ .

$\frac{x}{2 (x) - 8} \cdot \frac{3 x - 12}{5}$

Step 2.2

Factor $2$ out of $- 8$ .

$\frac{x}{2 x + 2 \cdot - 4} \cdot \frac{3 x - 12}{5}$

Step 2.3

Factor $2$ out of $2 x + 2 \cdot - 4$ .

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

Step 3

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

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Step 3.1

Factor $3$ out of $3 x$ .

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

Step 3.2

Factor $3$ out of $- 12$ .

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

Step 3.3

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

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

Step 4

Cancel the common factor of $x - 4$ .

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Step 4.1

Factor $x - 4$ out of $2 (x - 4)$ .

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

Step 4.2

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

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

$\frac{x}{2} \cdot \frac{3}{5}$

Step 5

Multiply $\frac{x}{2}$ by $\frac{3}{5}$ .

$\frac{x \cdot 3}{2 \cdot 5}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $2$ by $5$ .

$\frac{x \cdot 3}{10}$

Step 6.2

Move $3$ to the left of $x$ .

$\frac{3 x}{10}$