Simplify (m^2-n^2)/(4m+4n)*(m+n)/(m-n)

$\frac{m^{2} - n^{2}}{4 m + 4 n} \cdot \frac{m + n}{m - n}$

Step 1

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 $b = n$ .

$\frac{(m + n) (m - n)}{4 m + 4 n} \cdot \frac{m + n}{m - n}$

Step 2

Simplify terms.

Factor $4$ out of $4 m + 4 n$ .

Factor $4$ out of $4 m$ .

$\frac{(m + n) (m - n)}{4 (m) + 4 n} \cdot \frac{m + n}{m - n}$

Factor $4$ out of $4 n$ .

$\frac{(m + n) (m - n)}{4 (m) + 4 (n)} \cdot \frac{m + n}{m - n}$

Factor $4$ out of $4 (m) + 4 (n)$ .

$\frac{(m + n) (m - n)}{4 (m + n)} \cdot \frac{m + n}{m - n}$

Cancel the common factor of $m - n$ .

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

$\frac{(m - n) (m + n)}{4 (m + n)} \cdot \frac{m + n}{m - n}$

Cancel the common factor.

$\frac{(m - n) (m + n)}{4 (m + n)} \cdot \frac{m + n}{m - n}$

Rewrite the expression.

$\frac{m + n}{4 (m + n)} \cdot (m + n)$

Cancel the common factor of $m + n$ .

Factor $m + n$ out of $4 (m + n)$ .

$\frac{m + n}{(m + n) \cdot 4} \cdot (m + n)$

Cancel the common factor.

$\frac{m + n}{(m + n) \cdot 4} \cdot (m + n)$

Rewrite the expression.

$\frac{m + n}{4}$