Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{x - 6}{x^{2} - 6^{2}}$

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 $b = 6$ .

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

Step 3

Cancel the common factor of $x - 6$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{1}{x + 6}$