Precalculus Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

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 $a = x$ and $b = 2$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x + 2$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x - 2$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$1 (4 x - 8)$

Step 3.3

Multiply $4 x - 8$ by $1$ .

$4 x - 8$