Algebra Examples

$\frac{x^{2} - 4}{4 x - 8} \cdot \frac{4}{x - 2}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{x^{2} - 2^{2}}{4 x - 8} \cdot \frac{4}{x - 2}$

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $4 x$ .

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

Step 2.1.2

Factor $4$ out of $- 8$ .

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

Step 2.1.3

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

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

Step 2.2

Cancel the common factor of $x - 2$ .

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{x + 2}{x - 2}$