Pre-Algebra Examples

$\frac{4 x - 16}{5 x + 15} \div \frac{4 - x}{2 x + 6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 x - 16}{5 x + 15} \cdot \frac{2 x + 6}{4 - x}$

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 16}{5 x + 15} \cdot \frac{2 x + 6}{4 - x}$

Step 2.1.2

Factor $4$ out of $- 16$ .

$\frac{4 x + 4 \cdot - 4}{5 x + 15} \cdot \frac{2 x + 6}{4 - x}$

Step 2.1.3

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

$\frac{4 (x - 4)}{5 x + 15} \cdot \frac{2 x + 6}{4 - x}$

Step 2.2

Factor $5$ out of $5 x + 15$ .

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Step 2.2.1

Factor $5$ out of $5 x$ .

$\frac{4 (x - 4)}{5 (x) + 15} \cdot \frac{2 x + 6}{4 - x}$

Step 2.2.2

Factor $5$ out of $15$ .

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

Step 2.2.3

Factor $5$ out of $5 x + 5 \cdot 3$ .

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

Step 2.3

Factor $2$ out of $2 x + 6$ .

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Step 2.3.1

Factor $2$ out of $2 x$ .

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

Step 2.3.2

Factor $2$ out of $6$ .

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

Step 2.3.3

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

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

Step 2.4

Cancel the common factor of $x + 3$ .

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Step 2.4.1

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

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

Step 2.4.2

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

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

Step 2.4.3

Cancel the common factor.

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

Step 2.4.4

Rewrite the expression.

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

Step 2.5

Multiply $\frac{4 (x - 4)}{5}$ by $\frac{2}{4 - x}$ .

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

Step 2.6

Multiply $2$ by $4$ .

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

Step 2.7

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

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Step 2.7.1

Factor $- 1$ out of $x$ .

$\frac{8 (- 1 (- x) - 4)}{5 (4 - x)}$

Step 2.7.2

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

$\frac{8 (- 1 (- x) - 1 (4))}{5 (4 - x)}$

Step 2.7.3

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

$\frac{8 (- 1 (- x + 4))}{5 (4 - x)}$

Step 2.7.4

Reorder terms.

$\frac{8 (- 1 (- x + 4))}{5 (- x + 4)}$

Step 2.7.5

Cancel the common factor.

$\frac{8 (- 1 (- x + 4))}{5 (- x + 4)}$

Step 2.7.6

Rewrite the expression.

$\frac{8 \cdot (- 1)}{5}$

Step 3

Multiply $8$ by $- 1$ .

$\frac{- 8}{5}$

Step 4

Move the negative in front of the fraction.

$- \frac{8}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{5}$

Decimal Form:

$- 1.6$

Mixed Number Form:

$- 1 \frac{3}{5}$