Algebra Examples

$f (x) = \frac{- 5}{x^{2} - 2 x - 3}$

Step 1

Factor $x^{2} - 2 x - 3$ using the AC method.

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Step 1.1

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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Step 1.2

Write the factored form using these integers.

$f (x) = \frac{- 5}{(x - 3) (x + 1)}$

Step 2

Move the negative in front of the fraction.

$f (x) = - \frac{5}{(x - 3) (x + 1)}$

Step 3

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Step 4