Algebra Examples

$\frac{n^{2} - 7 n - 44}{n^{2} - 121}$

Step 1

Factor $n^{2} - 7 n - 44$ 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 $- 44$ and whose sum is $- 7$ .

$- 11, 4$

Step 1.2

Write the factored form using these integers.

$\frac{(n - 11) (n + 4)}{n^{2} - 121}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $121$ as $11^{2}$ .

$\frac{(n - 11) (n + 4)}{n^{2} - 11^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = n$ and $b = 11$ .

$\frac{(n - 11) (n + 4)}{(n + 11) (n - 11)}$

Step 3

Cancel the common factor of $n - 11$ .

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Step 3.1

Cancel the common factor.

$\frac{(n - 11) (n + 4)}{(n + 11) (n - 11)}$

Step 3.2

Rewrite the expression.

$\frac{n + 4}{n + 11}$