Precalculus Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \cos (x)$ and $b = 2$ .

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

Step 2

Cancel the common factor of $\cos (x) - 2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$\frac{1}{\cos (x) + 2}$