Precalculus Examples

$\frac{(x + 5) (x - 1)}{x^{2} + 9 x + 20}$

Step 1

Factor

$x^{2} + 9 x + 20$ 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

$20$ and whose sum is

$9$ .

$4, 5$

Step 1.2

Write the factored form using these integers.

$\frac{(x + 5) (x - 1)}{(x + 4) (x + 5)}$

Step 2

Reduce the expression

$\frac{(x + 5) (x - 1)}{(x + 4) (x + 5)}$ by cancelling the common factors.

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Step 2.1

Cancel the common factor.

$\frac{(x + 5) (x - 1)}{(x + 4) (x + 5)}$

Step 2.2

Rewrite the expression.

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

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