Simplify ((n-15)/(9n))/((15-n)/(3n^5))

$\frac{\frac{n - 15}{9 n}}{\frac{15 - n}{3 n^{5}}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{n - 15}{9 n} \cdot \frac{3 n^{5}}{15 - n}$

Cancel the common factor of $3 n$ .

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

$\frac{n - 15}{3 n (3)} \cdot \frac{3 n^{5}}{15 - n}$

Factor $3 n$ out of $3 n^{5}$ .

$\frac{n - 15}{3 n (3)} \cdot \frac{3 n (n^{4})}{15 - n}$

Cancel the common factor.

$\frac{n - 15}{3 n \cdot 3} \cdot \frac{3 n \cdot n^{4}}{15 - n}$

Rewrite the expression.

$\frac{n - 15}{3} \cdot \frac{n^{4}}{15 - n}$

Multiply $\frac{n - 15}{3}$ by $\frac{n^{4}}{15 - n}$ .

$\frac{(n - 15) n^{4}}{3 (15 - n)}$

Cancel the common factor of $n - 15$ and $15 - n$ .

Factor $- 1$ out of $n$ .

$\frac{(- 1 (- n) - 15) n^{4}}{3 (15 - n)}$

Rewrite $- 15$ as $- 1 (15)$ .

$\frac{(- 1 (- n) - 1 (15)) n^{4}}{3 (15 - n)}$

Factor $- 1$ out of $- 1 (- n) - 1 (15)$ .

$\frac{- 1 (- n + 15) n^{4}}{3 (15 - n)}$

Reorder terms.

$\frac{- 1 (- n + 15) n^{4}}{3 (- n + 15)}$

Cancel the common factor.

$\frac{- 1 (- n + 15) n^{4}}{3 (- n + 15)}$

Rewrite the expression.

$\frac{- 1 n^{4}}{3}$

Move the negative in front of the fraction.

$- \frac{n^{4}}{3}$