Algebra Examples

$\frac{3 x - 12}{x + 5} \cdot \frac{x + 6}{2 x - 8}$

Step 1

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

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 12}{x + 5} \cdot \frac{x + 6}{2 x - 8}$

Step 1.2

Factor $3$ out of $- 12$ .

$\frac{3 x + 3 \cdot - 4}{x + 5} \cdot \frac{x + 6}{2 x - 8}$

Step 1.3

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

$\frac{3 (x - 4)}{x + 5} \cdot \frac{x + 6}{2 x - 8}$

Step 2

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

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Step 2.1

Factor $2$ out of $2 x$ .

$\frac{3 (x - 4)}{x + 5} \cdot \frac{x + 6}{2 (x) - 8}$

Step 2.2

Factor $2$ out of $- 8$ .

$\frac{3 (x - 4)}{x + 5} \cdot \frac{x + 6}{2 x + 2 \cdot - 4}$

Step 2.3

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

$\frac{3 (x - 4)}{x + 5} \cdot \frac{x + 6}{2 (x - 4)}$

Step 3

Cancel the common factor of $x - 4$ .

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Step 3.1

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

$\frac{(x - 4) \cdot 3}{x + 5} \cdot \frac{x + 6}{2 (x - 4)}$

Step 3.2

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

$\frac{(x - 4) \cdot 3}{x + 5} \cdot \frac{x + 6}{(x - 4) \cdot 2}$

Step 3.3

Cancel the common factor.

$\frac{(x - 4) \cdot 3}{x + 5} \cdot \frac{x + 6}{(x - 4) \cdot 2}$

Step 3.4

Rewrite the expression.

$\frac{3}{x + 5} \cdot \frac{x + 6}{2}$

Step 4

Multiply $\frac{3}{x + 5}$ by $\frac{x + 6}{2}$ .

$\frac{3 (x + 6)}{(x + 5) \cdot 2}$

Step 5

Move $2$ to the left of $x + 5$ .

$\frac{3 (x + 6)}{2 (x + 5)}$