Precalculus Examples

$\frac{x - 4}{x^{2} - 3 x - 4}$

Step 1

Factor $x^{2} - 3 x - 4$ 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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Step 1.2

Write the factored form using these integers.

$\frac{x - 4}{(x - 4) (x + 1)}$

Step 2

Cancel the common factor of $x - 4$ .

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Step 2.1

Cancel the common factor.

$\frac{x - 4}{(x - 4) (x + 1)}$

Step 2.2

Rewrite the expression.

$\frac{1}{x + 1}$