Precalculus Examples

$\frac{x^{2} + 12 x + 12}{x^{3} - 4 x}$

Step 1

Factor $x$ out of $x^{3} - 4 x$ .

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Step 1.1

Factor $x$ out of $x^{3}$ .

$\frac{x^{2} + 12 x + 12}{x \cdot x^{2} - 4 x}$

Step 1.2

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

$\frac{x^{2} + 12 x + 12}{x \cdot x^{2} + x \cdot - 4}$

Step 1.3

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

$\frac{x^{2} + 12 x + 12}{x (x^{2} - 4)}$

Step 2

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

$\frac{x^{2} + 12 x + 12}{x (x^{2} - 2^{2})}$

Step 3

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 $b = 2$ .

$\frac{x^{2} + 12 x + 12}{x (x + 2) (x - 2)}$