Simplify ((m^2-n^2)/(m+n))/(m/(m^2+nm))

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

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 $b = n$ .

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

Step 3

Simplify terms.

Cancel the common factor of $m + n$ .

Cancel the common factor.

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

Divide $m - n$ by $1$ .

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

Factor $m$ out of $m^{2} + n m$ .

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

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

Factor $m$ out of $n m$ .

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

Factor $m$ out of $m \cdot m + m n$ .

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

Cancel the common factor of $m$ .

Cancel the common factor.

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

Divide $m + n$ by $1$ .

$(m - n) (m + n)$

Step 4

Expand $(m - n) (m + n)$ using the FOIL Method.

Apply the distributive property.

$m (m + n) - n (m + n)$

Apply the distributive property.

$m \cdot m + m n - n (m + n)$

Apply the distributive property.

$m \cdot m + m n - n m - n \cdot n$

Step 5

Simplify terms.

Combine the opposite terms in $m \cdot m + m n - n m - n \cdot n$ .

Reorder the factors in the terms $m n$ and $- n m$ .

$m \cdot m + m n - m n - n \cdot n$

Subtract $m n$ from $m n$ .

$m \cdot m + 0 - n \cdot n$

Add $m \cdot m$ and $0$ .

$m \cdot m - n \cdot n$

Simplify each term.

Multiply $m$ by $m$ .

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

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

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

Multiply $n$ by $n$ .

$m^{2} - n^{2}$

Simplify ((m^2-n^2)/(m+n))/(m/(m^2+nm))

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