Algebra Examples

$y = \frac{x}{x^{2} - 9}$

Step 1

Simplify the denominator.

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Step 1.1

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

$y = \frac{x}{x^{2} - 3^{2}}$

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 $b = 3$ .

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

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Decreasing on: $(- \infty, - 3), (- 3, 3), (3, \infty)$

Step 3