Trigonometry Examples

$\frac{x^{2} - 4}{x - 2} = x + 2$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{x^{2} - 2^{2}}{x - 2} = x + 2$

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 $a = x$ and $b = 2$ .

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

Step 2

Cancel the common factor of $x - 2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $x + 2$ by $1$ .

$x + 2 = x + 2$

Step 3

Since the two sides have been shown to be equivalent, the equation is an identity.

$\frac{x^{2} - 4}{x - 2} = x + 2$ is an identity.