Simplify (3m^2-3n^2)/(6m+6n)

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

Step 1

Cancel the common factor of $3 m^{2} - 3 n^{2}$ and $6 m + 6 n$ .

Factor $3$ out of $3 m^{2}$ .

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

Factor $3$ out of $- 3 n^{2}$ .

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

Factor $3$ out of $3 (m^{2}) + 3 (- n^{2})$ .

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

Cancel the common factors.

Factor $3$ out of $6 m$ .

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

Factor $3$ out of $6 n$ .

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

Factor $3$ out of $3 (2 m) + 3 (2 n)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{m^{2} - n^{2}}{2 m + 2 n}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = n$ .

$\frac{(m + n) (m - n)}{2 m + 2 n}$

Step 3

Simplify terms.

Factor $2$ out of $2 m + 2 n$ .

Factor $2$ out of $2 m$ .

$\frac{(m + n) (m - n)}{2 (m) + 2 n}$

Factor $2$ out of $2 n$ .

$\frac{(m + n) (m - n)}{2 (m) + 2 (n)}$

Factor $2$ out of $2 (m) + 2 (n)$ .

$\frac{(m + n) (m - n)}{2 (m + n)}$

Cancel the common factor of $m + n$ .

Cancel the common factor.

$\frac{(m + n) (m - n)}{2 (m + n)}$

Rewrite the expression.

$\frac{m - n}{2}$