Algebra Examples

$\frac{x^{2} - 6 x}{x^{2} - 36} \cdot \frac{x + 6}{x^{2}}$

Step 1

Factor $x$ out of $x^{2} - 6 x$ .

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Step 1.1

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

$\frac{x \cdot x - 6 x}{x^{2} - 36} \cdot \frac{x + 6}{x^{2}}$

Step 1.2

Factor $x$ out of $- 6 x$ .

$\frac{x \cdot x + x \cdot - 6}{x^{2} - 36} \cdot \frac{x + 6}{x^{2}}$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot - 6$ .

$\frac{x (x - 6)}{x^{2} - 36} \cdot \frac{x + 6}{x^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{x (x - 6)}{x^{2} - 6^{2}} \cdot \frac{x + 6}{x^{2}}$

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 $b = 6$ .

$\frac{x (x - 6)}{(x + 6) (x - 6)} \cdot \frac{x + 6}{x^{2}}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

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

$\frac{x (x - 6)}{(x + 6) (x - 6)} \cdot \frac{x + 6}{x \cdot x}$

Step 3.1.2

Cancel the common factor.

$\frac{x (x - 6)}{(x + 6) (x - 6)} \cdot \frac{x + 6}{x \cdot x}$

Step 3.1.3

Rewrite the expression.

$\frac{x - 6}{(x + 6) (x - 6)} \cdot \frac{x + 6}{x}$

Step 3.2

Cancel the common factor of $x + 6$ .

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Step 3.2.1

Cancel the common factor.

$\frac{x - 6}{(x + 6) (x - 6)} \cdot \frac{x + 6}{x}$

Step 3.2.2

Rewrite the expression.

$\frac{x - 6}{x - 6} \cdot \frac{1}{x}$

Step 3.3

Multiply $\frac{x - 6}{x - 6}$ by $\frac{1}{x}$ .

$\frac{x - 6}{(x - 6) x}$

Step 3.4

Cancel the common factor of $x - 6$ .

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Step 3.4.1

Cancel the common factor.

$\frac{x - 6}{(x - 6) x}$

Step 3.4.2

Rewrite the expression.

$\frac{1}{x}$