Simplify (n^2-9)/(n+3)*n/(2n-6)

$\frac{n^{2} - 9}{n + 3} \cdot \frac{n}{2 n - 6}$

Step 1

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{n^{2} - 3^{2}}{n + 3} \cdot \frac{n}{2 n - 6}$

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 $b = 3$ .

$\frac{(n + 3) (n - 3)}{n + 3} \cdot \frac{n}{2 n - 6}$

Step 2

Simplify terms.

Factor $2$ out of $2 n - 6$ .

Factor $2$ out of $2 n$ .

$\frac{(n + 3) (n - 3)}{n + 3} \cdot \frac{n}{2 (n) - 6}$

Factor $2$ out of $- 6$ .

$\frac{(n + 3) (n - 3)}{n + 3} \cdot \frac{n}{2 n + 2 \cdot - 3}$

Factor $2$ out of $2 n + 2 \cdot - 3$ .

$\frac{(n + 3) (n - 3)}{n + 3} \cdot \frac{n}{2 (n - 3)}$

Cancel the common factor of $n - 3$ .

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

$\frac{(n - 3) (n + 3)}{n + 3} \cdot \frac{n}{2 (n - 3)}$

Factor $n - 3$ out of $2 (n - 3)$ .

$\frac{(n - 3) (n + 3)}{n + 3} \cdot \frac{n}{(n - 3) \cdot 2}$

Cancel the common factor.

$\frac{(n - 3) (n + 3)}{n + 3} \cdot \frac{n}{(n - 3) \cdot 2}$

Rewrite the expression.

$\frac{n + 3}{n + 3} \cdot \frac{n}{2}$

Multiply $\frac{n + 3}{n + 3}$ by $\frac{n}{2}$ .

$\frac{(n + 3) n}{(n + 3) \cdot 2}$

Cancel the common factor of $n + 3$ .

Cancel the common factor.

$\frac{(n + 3) n}{(n + 3) \cdot 2}$

Rewrite the expression.

$\frac{n}{2}$