Algebra Examples

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

Step 1

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

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

Step 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 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Reduce the expression $\frac{(\cos (x) + 2) (\cos (x) - 2)}{\cos (x) - 2}$ by cancelling the common factors.

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Divide $\cos (x) + 2$ by $1$ .

$\cos (x) + 2$