Calculus Examples

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

Step 1

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

$f (x) = \frac{x^{2} - 2^{2}}{x - 2}$

Step 2

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

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$f (x) = \frac{x + 2}{1}$

Step 3.2

Divide $x + 2$ by $1$ .

$f (x) = x + 2$