Algebra Examples

$\frac{6 n + 6}{n + 9} \cdot \frac{n^{2} + 6 n - 27}{6 n + 6}$

Step 1

Factor $6$ out of $6 n + 6$ .

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Step 1.1

Factor $6$ out of $6 n$ .

$\frac{6 (n) + 6}{n + 9} \cdot \frac{n^{2} + 6 n - 27}{6 n + 6}$

Step 1.2

Factor $6$ out of $6$ .

$\frac{6 (n) + 6 (1)}{n + 9} \cdot \frac{n^{2} + 6 n - 27}{6 n + 6}$

Step 1.3

Factor $6$ out of $6 (n) + 6 (1)$ .

$\frac{6 (n + 1)}{n + 9} \cdot \frac{n^{2} + 6 n - 27}{6 n + 6}$

Step 2

Factor $n^{2} + 6 n - 27$ using the AC method.

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Step 2.1

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 $- 27$ and whose sum is $6$ .

$- 3, 9$

Step 2.2

Write the factored form using these integers.

$\frac{6 (n + 1)}{n + 9} \cdot \frac{(n - 3) (n + 9)}{6 n + 6}$

Step 3

Simplify terms.

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Step 3.1

Factor $6$ out of $6 n + 6$ .

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Step 3.1.1

Factor $6$ out of $6 n$ .

$\frac{6 (n + 1)}{n + 9} \cdot \frac{(n - 3) (n + 9)}{6 (n) + 6}$

Step 3.1.2

Factor $6$ out of $6$ .

$\frac{6 (n + 1)}{n + 9} \cdot \frac{(n - 3) (n + 9)}{6 (n) + 6 (1)}$

Step 3.1.3

Factor $6$ out of $6 (n) + 6 (1)$ .

$\frac{6 (n + 1)}{n + 9} \cdot \frac{(n - 3) (n + 9)}{6 (n + 1)}$

Step 3.2

Cancel the common factor of $6 (n + 1)$ .

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Step 3.2.1

Cancel the common factor.

$\frac{6 (n + 1)}{n + 9} \cdot \frac{(n - 3) (n + 9)}{6 (n + 1)}$

Step 3.2.2

Rewrite the expression.

$\frac{1}{n + 9} \cdot ((n - 3) (n + 9))$

Step 3.3

Cancel the common factor of $n + 9$ .

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Step 3.3.1

Factor $n + 9$ out of $(n - 3) (n + 9)$ .

$\frac{1}{n + 9} \cdot ((n + 9) (n - 3))$

Step 3.3.2

Cancel the common factor.

$\frac{1}{n + 9} \cdot ((n + 9) (n - 3))$

Step 3.3.3

Rewrite the expression.

$n - 3$