Basic Math Examples

$\frac{4 w - 16}{4 w - 8} \cdot \frac{w}{w^{2} - 16}$

Step 1

Simplify with factoring out.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $4 w$ .

$\frac{4 (w) - 16}{4 w - 8} \cdot \frac{w}{w^{2} - 16}$

Step 1.1.2

Factor $4$ out of $- 16$ .

$\frac{4 w + 4 \cdot - 4}{4 w - 8} \cdot \frac{w}{w^{2} - 16}$

Step 1.1.3

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

$\frac{4 (w - 4)}{4 w - 8} \cdot \frac{w}{w^{2} - 16}$

Step 1.2

Factor $4$ out of $4 w - 8$ .

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Step 1.2.1

Factor $4$ out of $4 w$ .

$\frac{4 (w - 4)}{4 (w) - 8} \cdot \frac{w}{w^{2} - 16}$

Step 1.2.2

Factor $4$ out of $- 8$ .

$\frac{4 (w - 4)}{4 w + 4 \cdot - 2} \cdot \frac{w}{w^{2} - 16}$

Step 1.2.3

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

$\frac{4 (w - 4)}{4 (w - 2)} \cdot \frac{w}{w^{2} - 16}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{4 (w - 4)}{4 (w - 2)} \cdot \frac{w}{w^{2} - 4^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = w$ and $b = 4$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $w - 4$ .

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Step 3.1.1

Factor $w - 4$ out of $4 (w - 4)$ .

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

Step 3.1.2

Factor $w - 4$ out of $(w + 4) (w - 4)$ .

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

Multiply $\frac{4}{4 (w - 2)}$ by $\frac{w}{w + 4}$ .

$\frac{4 w}{4 (w - 2) (w + 4)}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

$\frac{4 w}{4 (w - 2) (w + 4)}$

Step 3.3.2

Rewrite the expression.

$\frac{w}{(w - 2) (w + 4)}$