Algebra Examples

$\frac{3 x + 12}{4 x - 16} \cdot \frac{8 - 2 x}{x + 4}$

Step 1

Simplify terms.

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Step 1.1

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

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 12}{4 x - 16} \cdot \frac{8 - 2 x}{x + 4}$

Step 1.1.2

Factor $3$ out of $12$ .

$\frac{3 x + 3 \cdot 4}{4 x - 16} \cdot \frac{8 - 2 x}{x + 4}$

Step 1.1.3

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

$\frac{3 (x + 4)}{4 x - 16} \cdot \frac{8 - 2 x}{x + 4}$

Step 1.2

Factor $4$ out of $4 x - 16$ .

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Step 1.2.1

Factor $4$ out of $4 x$ .

$\frac{3 (x + 4)}{4 (x) - 16} \cdot \frac{8 - 2 x}{x + 4}$

Step 1.2.2

Factor $4$ out of $- 16$ .

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

Step 1.2.3

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

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

Step 1.3

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

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Step 1.3.1

Factor $2$ out of $8$ .

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.4

Cancel the common factor of $x + 4$ .

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Step 1.4.1

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

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

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

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 1.6

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

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

Step 1.7

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

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Step 1.7.1

Rewrite $4$ as $- 1 (- 4)$ .

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

Step 1.7.2

Factor $- 1$ out of $- x$ .

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

Step 1.7.3

Factor $- 1$ out of $- 1 (- 4) - (x)$ .

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

Step 1.7.4

Reorder terms.

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

Step 1.7.5

Cancel the common factor.

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

Step 1.7.6

Rewrite the expression.

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

Step 2

Multiply $3$ by $- 1$ .

$\frac{- 3}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

$- 1 \frac{1}{2}$