Pre-Algebra Examples

$f (x) = \frac{1}{x^{2} - x - 6}$

Step 1

Rewrite the function as an equation.

$y = \frac{1}{x^{2} - x - 6}$

Step 2

Factor $x^{2} - x - 6$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 2.2

Write the factored form using these integers.

$y = \frac{1}{(x - 3) (x + 2)}$