Simplify (n^5)/(n-6)*(n^2-6n)/(n^8)

$\frac{n^{5}}{n - 6} \cdot \frac{n^{2} - 6 n}{n^{8}}$

Step 1

Factor $n$ out of $n^{2} - 6 n$ .

Factor $n$ out of $n^{2}$ .

$\frac{n^{5}}{n - 6} \cdot \frac{n \cdot n - 6 n}{n^{8}}$

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

$\frac{n^{5}}{n - 6} \cdot \frac{n \cdot n + n \cdot - 6}{n^{8}}$

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

$\frac{n^{5}}{n - 6} \cdot \frac{n (n - 6)}{n^{8}}$

Step 2

Cancel the common factor of $n^{5}$ .

Factor $n^{5}$ out of $n^{8}$ .

$\frac{n^{5}}{n - 6} \cdot \frac{n (n - 6)}{n^{5} n^{3}}$

Cancel the common factor.

$\frac{n^{5}}{n - 6} \cdot \frac{n (n - 6)}{n^{5} n^{3}}$

Rewrite the expression.

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

Step 3

Cancel the common factor of $n - 6$ .

Factor $n - 6$ out of $n (n - 6)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $n$ and $n^{3}$ .

Raise $n$ to the power of $1$ .

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

Factor $n$ out of $n^{1}$ .

$\frac{n \cdot 1}{n^{3}}$

Cancel the common factors.

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

$\frac{n \cdot 1}{n \cdot n^{2}}$

Cancel the common factor.

$\frac{n \cdot 1}{n \cdot n^{2}}$

Rewrite the expression.

$\frac{1}{n^{2}}$