Simplify ((m^2+m-mn-n)/(m^2+m+mn+n))÷((m^2-m-mn+n)/(m^2-m+mn-n))

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

To divide by a fraction, multiply by its reciprocal.

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

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$\frac{m (m + 1) - n (m + 1)}{m^{2} + m + m n + n} \cdot \frac{m^{2} - m + m n - n}{m^{2} - m - m n + n}$

Factor the polynomial by factoring out the greatest common factor, $m + 1$ .

$\frac{(m + 1) (m - n)}{m^{2} + m + m n + n} \cdot \frac{m^{2} - m + m n - n}{m^{2} - m - m n + n}$

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(m + 1) (m - n)}{(m^{2} + m) + m n + n} \cdot \frac{m^{2} - m + m n - n}{m^{2} - m - m n + n}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(m + 1) (m - n)}{m (m + 1) + n (m + 1)} \cdot \frac{m^{2} - m + m n - n}{m^{2} - m - m n + n}$

Factor the polynomial by factoring out the greatest common factor, $m + 1$ .

$\frac{(m + 1) (m - n)}{(m + 1) (m + n)} \cdot \frac{m^{2} - m + m n - n}{m^{2} - m - m n + n}$

Cancel the common factor of $m + 1$ .

Cancel the common factor.

$\frac{(m + 1) (m - n)}{(m + 1) (m + n)} \cdot \frac{m^{2} - m + m n - n}{m^{2} - m - m n + n}$

Rewrite the expression.

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

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$\frac{m - n}{m + n} \cdot \frac{m (m - 1) + n (m - 1)}{m^{2} - m - m n + n}$

Factor the polynomial by factoring out the greatest common factor, $m - 1$ .

$\frac{m - n}{m + n} \cdot \frac{(m - 1) (m + n)}{m^{2} - m - m n + n}$

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{m - n}{m + n} \cdot \frac{(m - 1) (m + n)}{(m^{2} - m) - m n + n}$

Factor out the greatest common factor (GCF) from each group.

$\frac{m - n}{m + n} \cdot \frac{(m - 1) (m + n)}{m (m - 1) - n (m - 1)}$

Factor the polynomial by factoring out the greatest common factor, $m - 1$ .

$\frac{m - n}{m + n} \cdot \frac{(m - 1) (m + n)}{(m - 1) (m - n)}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $m - n$ .

Factor $m - n$ out of $(m - 1) (m - n)$ .

$\frac{m - n}{m + n} \cdot \frac{(m - 1) (m + n)}{(m - n) (m - 1)}$

Cancel the common factor.

$\frac{m - n}{m + n} \cdot \frac{(m - 1) (m + n)}{(m - n) (m - 1)}$

Rewrite the expression.

$\frac{1}{m + n} \cdot \frac{(m - 1) (m + n)}{m - 1}$

Cancel the common factor of $m + n$ .

Factor $m + n$ out of $(m - 1) (m + n)$ .

$\frac{1}{m + n} \cdot \frac{(m + n) (m - 1)}{m - 1}$

Cancel the common factor.

$\frac{1}{m + n} \cdot \frac{(m + n) (m - 1)}{m - 1}$

Rewrite the expression.

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

Cancel the common factor of $m - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$1$

Simplify ((m^2+m-mn-n)/(m^2+m+mn+n))÷((m^2-m-mn+n)/(m^2-m+mn-n))

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