Simplify ((n+3)/(2n-6))÷((n+3)/(3n-9))

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

To divide by a fraction, multiply by its reciprocal.

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

Cancel the common factor of $n + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 n - 6} (3 n - 9)$

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

Factor $2$ out of $2 n$ .

$\frac{1}{2 (n) - 6} (3 n - 9)$

Factor $2$ out of $- 6$ .

$\frac{1}{2 n + 2 \cdot - 3} (3 n - 9)$

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

$\frac{1}{2 (n - 3)} (3 n - 9)$

Multiply $\frac{1}{2 (n - 3)}$ by $3 n - 9$ .

$\frac{3 n - 9}{2 (n - 3)}$

Factor $3$ out of $3 n - 9$ .

Factor $3$ out of $3 n$ .

$\frac{3 (n) - 9}{2 (n - 3)}$

Factor $3$ out of $- 9$ .

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

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

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

Cancel the common factor of $n - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$