Precalculus Examples

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

Step 1

Factor $x$ out of $x^{2} - 2 x$ .

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Step 1.1

Factor $x$ out of $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{x (x - 2)}{x^{2} - 2^{2}}$

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 $b = 2$ .

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

Step 3

Cancel the common factor of $x - 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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