Simplify (10m^5n^2-30mn)/(5mn)

$\frac{10 m^{5} n^{2} - 30 m n}{5 m n}$

Step 1

Factor $10 m n$ out of $10 m^{5} n^{2} - 30 m n$ .

Factor $10 m n$ out of $10 m^{5} n^{2}$ .

$\frac{10 m n (m^{4} n) - 30 m n}{5 m n}$

Factor $10 m n$ out of $- 30 m n$ .

$\frac{10 m n (m^{4} n) + 10 m n (- 3)}{5 m n}$

Factor $10 m n$ out of $10 m n (m^{4} n) + 10 m n (- 3)$ .

$\frac{10 m n (m^{4} n - 3)}{5 m n}$

Step 2

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 m n (m^{4} n - 3)$ .

$\frac{5 (2 m n (m^{4} n - 3))}{5 m n}$

Cancel the common factors.

Factor $5$ out of $5 m n$ .

$\frac{5 (2 m n (m^{4} n - 3))}{5 (m n)}$

Cancel the common factor.

$\frac{5 (2 m n (m^{4} n - 3))}{5 (m n)}$

Rewrite the expression.

$\frac{2 m n (m^{4} n - 3)}{m n}$

Step 3

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{2 m n (m^{4} n - 3)}{m n}$

Rewrite the expression.

$\frac{2 n (m^{4} n - 3)}{n}$

Step 4

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{2 n (m^{4} n - 3)}{n}$

Divide $2 (m^{4} n - 3)$ by $1$ .

$2 (m^{4} n - 3)$

Step 5

Apply the distributive property.

$2 (m^{4} n) + 2 \cdot - 3$

Step 6

Multiply $2$ by $- 3$ .

$2 m^{4} n - 6$