Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

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

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

Step 1.3

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 $b = 2$ .

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

Step 2

Cancel the common factor of $x + 2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $x (x - 2)$ by $1$ .

$x (x - 2)$

Step 3

Apply the distributive property.

$x \cdot x + x \cdot - 2$

Step 4

Multiply $x$ by $x$ .

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

Step 5

Move $- 2$ to the left of $x$ .

$x^{2} - 2 x$