Precalculus Examples

$\frac{3 x - 6}{5 x - 20} \cdot \frac{x - 8}{5 x - 10}$

Step 1

Factor $3$ out of $3 x - 6$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{5 x - 20} \cdot \frac{x - 8}{5 x - 10}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{5 x - 20} \cdot \frac{x - 8}{5 x - 10}$

Step 1.3

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

$\frac{3 (x - 2)}{5 x - 20} \cdot \frac{x - 8}{5 x - 10}$

Step 2

Factor $5$ out of $5 x - 20$ .

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Step 2.1

Factor $5$ out of $5 x$ .

$\frac{3 (x - 2)}{5 (x) - 20} \cdot \frac{x - 8}{5 x - 10}$

Step 2.2

Factor $5$ out of $- 20$ .

$\frac{3 (x - 2)}{5 x + 5 \cdot - 4} \cdot \frac{x - 8}{5 x - 10}$

Step 2.3

Factor $5$ out of $5 x + 5 \cdot - 4$ .

$\frac{3 (x - 2)}{5 (x - 4)} \cdot \frac{x - 8}{5 x - 10}$

Step 3

Factor $5$ out of $5 x - 10$ .

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Step 3.1

Factor $5$ out of $5 x$ .

$\frac{3 (x - 2)}{5 (x - 4)} \cdot \frac{x - 8}{5 (x) - 10}$

Step 3.2

Factor $5$ out of $- 10$ .

$\frac{3 (x - 2)}{5 (x - 4)} \cdot \frac{x - 8}{5 x + 5 \cdot - 2}$

Step 3.3

Factor $5$ out of $5 x + 5 \cdot - 2$ .

$\frac{3 (x - 2)}{5 (x - 4)} \cdot \frac{x - 8}{5 (x - 2)}$

Step 4

Cancel the common factor of $x - 2$ .

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Step 4.1

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

$\frac{(x - 2) \cdot 3}{5 (x - 4)} \cdot \frac{x - 8}{5 (x - 2)}$

Step 4.2

Factor $x - 2$ out of $5 (x - 2)$ .

$\frac{(x - 2) \cdot 3}{5 (x - 4)} \cdot \frac{x - 8}{(x - 2) \cdot 5}$

Step 4.3

Cancel the common factor.

$\frac{(x - 2) \cdot 3}{5 (x - 4)} \cdot \frac{x - 8}{(x - 2) \cdot 5}$

Step 4.4

Rewrite the expression.

$\frac{3}{5 (x - 4)} \cdot \frac{x - 8}{5}$

Step 5

Multiply $\frac{3}{5 (x - 4)}$ by $\frac{x - 8}{5}$ .

$\frac{3 (x - 8)}{5 (x - 4) \cdot 5}$

Step 6

Multiply $5$ by $5$ .

$\frac{3 (x - 8)}{25 (x - 4)}$