Simplify (n+6)/(27n^2-54n)-(n-3)/(27n^2-54n)

$\frac{n + 6}{27 n^{2} - 54 n} - \frac{n - 3}{27 n^{2} - 54 n}$

Combine the numerators over the common denominator.

$\frac{n + 6 - (n - 3)}{27 n^{2} - 54 n}$

Simplify each term.

Apply the distributive property.

$\frac{n + 6 - n - - 3}{27 n^{2} - 54 n}$

Multiply $- 1$ by $- 3$ .

$\frac{n + 6 - n + 3}{27 n^{2} - 54 n}$

Simplify terms.

Combine the opposite terms in $n + 6 - n + 3$ .

Subtract $n$ from $n$ .

$\frac{0 + 6 + 3}{27 n^{2} - 54 n}$

Add $0$ and $6$ .

$\frac{6 + 3}{27 n^{2} - 54 n}$

Add $6$ and $3$ .

$\frac{9}{27 n^{2} - 54 n}$

Factor $27 n$ out of $27 n^{2} - 54 n$ .

Factor $27 n$ out of $27 n^{2}$ .

$\frac{9}{27 n (n) - 54 n}$

Factor $27 n$ out of $- 54 n$ .

$\frac{9}{27 n (n) + 27 n (- 2)}$

Factor $27 n$ out of $27 n (n) + 27 n (- 2)$ .

$\frac{9}{27 n (n - 2)}$

Cancel the common factor of $9$ and $27$ .

Factor $9$ out of $9$ .

$\frac{9 (1)}{27 n (n - 2)}$

Cancel the common factors.

Factor $9$ out of $27 n (n - 2)$ .

$\frac{9 (1)}{9 (3 n (n - 2))}$

Cancel the common factor.

$\frac{9 \cdot 1}{9 (3 n (n - 2))}$

Rewrite the expression.

$\frac{1}{3 n (n - 2)}$