Algebra Examples

Simplify the expression $\frac{2 x^{3} - 32 x}{2 (x^{2} - 4 x)}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $2 x$ out of $2 x^{3} - 32 x$ .

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Step 1.1.1

Factor $2 x$ out of $2 x^{3}$ .

$\frac{2 x (x^{2}) - 32 x}{2 (x^{2} - 4 x)}$

Step 1.1.2

Factor $2 x$ out of $- 32 x$ .

$\frac{2 x (x^{2}) + 2 x (- 16)}{2 (x^{2} - 4 x)}$

Step 1.1.3

Factor $2 x$ out of $2 x (x^{2}) + 2 x (- 16)$ .

$\frac{2 x (x^{2} - 16)}{2 (x^{2} - 4 x)}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

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

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 $b = 4$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $x - 4$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $x + 4$ by $1$ .

$x + 4$