Algebra Examples

$\frac{n - 2}{n^{2} - 13 n + 40} (n - 5)$

Step 1

Factor $n^{2} - 13 n + 40$ 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 $40$ and whose sum is $- 13$ .

$- 8, - 5$

Step 1.2

Write the factored form using these integers.

$\frac{n - 2}{(n - 8) (n - 5)} \cdot (n - 5)$

Step 2

Cancel the common factor of $n - 5$ .

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Step 2.1

Factor $n - 5$ out of $(n - 8) (n - 5)$ .

$\frac{n - 2}{(n - 5) (n - 8)} \cdot (n - 5)$

Step 2.2

Cancel the common factor.

$\frac{n - 2}{(n - 5) (n - 8)} \cdot (n - 5)$

Step 2.3

Rewrite the expression.

$\frac{n - 2}{n - 8}$