Trigonometry Examples

$f (x) = \frac{x - 3}{x^{2} - 9}$

Step 1

Rewrite $9$ as $3^{2}$ .

$f (x) = \frac{x - 3}{x^{2} - 3^{2}}$

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 $b = 3$ .

$f (x) = \frac{x - 3}{(x + 3) (x - 3)}$

Step 3

Reduce the expression $\frac{x - 3}{(x + 3) (x - 3)}$ by cancelling the common factors.

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Step 3.1

Cancel the common factor.

$f (x) = \frac{x - 3}{(x + 3) (x - 3)}$

Step 3.2

Rewrite the expression.

$f (x) = \frac{1}{x + 3}$