Simplify (m-3n)/(6m^3n)-(m+3n)/(6m^3n)

$\frac{m - 3 n}{6 m^{3} n} - \frac{m + 3 n}{6 m^{3} n}$

Step 1

Combine the numerators over the common denominator.

$\frac{m - 3 n - (m + 3 n)}{6 m^{3} n}$

Step 2

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

$\frac{m - 3 n - m - 3 n}{6 m^{3} n}$

Step 3

Simplify terms.

Combine the opposite terms in $m - 3 n - m - 3 n$ .

Subtract $m$ from $m$ .

$\frac{- 3 n + 0 - 3 n}{6 m^{3} n}$

Add $- 3 n$ and $0$ .

$\frac{- 3 n - 3 n}{6 m^{3} n}$

Subtract $3 n$ from $- 3 n$ .

$\frac{- 6 n}{6 m^{3} n}$

Cancel the common factor of $- 6$ and $6$ .

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

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

Cancel the common factors.

Factor $6$ out of $6 m^{3} n$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $n$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{m^{3}}$

Move the negative in front of the fraction.

$- \frac{1}{m^{3}}$