Simplify (6n+6)/(n+9)*(n^2+6n-27)/(6n+6)

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

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

Factor $6$ out of $6 n$ .

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

Factor $6$ out of $6$ .

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

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

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

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

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 $6$ .

$- 3, 9$

Write the factored form using these integers.

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

Simplify terms.

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

Factor $6$ out of $6 n$ .

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

Factor $6$ out of $6$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $n + 9$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$n - 3$

Simplify (6n+6)/(n+9)*(n^2+6n-27)/(6n+6)

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