Divide (4/(n-6))÷((4n)/(8n-48))

$\frac{4}{n - 6} \div \frac{4 n}{8 n - 48}$

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{n - 6} \cdot \frac{8 n - 48}{4 n}$

Cancel the common factor of $4$ .

Factor $4$ out of $4 n$ .

$\frac{4}{n - 6} \cdot \frac{8 n - 48}{4 (n)}$

Cancel the common factor.

$\frac{4}{n - 6} \cdot \frac{8 n - 48}{4 n}$

Rewrite the expression.

$\frac{1}{n - 6} \cdot \frac{8 n - 48}{n}$

Multiply $\frac{1}{n - 6}$ by $\frac{8 n - 48}{n}$ .

$\frac{8 n - 48}{(n - 6) n}$

Factor $8$ out of $8 n - 48$ .

Factor $8$ out of $8 n$ .

$\frac{8 (n) - 48}{(n - 6) n}$

Factor $8$ out of $- 48$ .

$\frac{8 n + 8 \cdot - 6}{(n - 6) n}$

Factor $8$ out of $8 n + 8 \cdot - 6$ .

$\frac{8 (n - 6)}{(n - 6) n}$

Cancel the common factor of $n - 6$ .

Cancel the common factor.

$\frac{8 (n - 6)}{(n - 6) n}$

Rewrite the expression.

$\frac{8}{n}$