Solve (m+n)^2/mn-m^2-n^2/mn

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

Evaluate

$$\frac{2\left(m+n\right)}{m}$$

Short Solution Steps

Since \frac{\left(m+n\right)^{2}}{mn} and \frac{m^{2}-n^{2}}{mn} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(m+n\right)^{2}-\left(m^{2}-n^{2}\right).

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

Combine like terms in m^{2}+2mn+n^{2}-m^{2}+n^{2}.

$$\frac{2n^{2}+2mn}{mn}$$

Factor the expressions that are not already factored in \frac{2n^{2}+2mn}{mn}.

$$\frac{2n\left(m+n\right)}{mn}$$

Cancel out n in both numerator and denominator.

$$\frac{2\left(m+n\right)}{m}$$

Use the distributive property to multiply 2 by m+n.

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

Expand

$$\frac{2\left(m+n\right)}{m}$$

Short Solution Steps

Since \frac{\left(m+n\right)^{2}}{mn} and \frac{m^{2}-n^{2}}{mn} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(m+n\right)^{2}-\left(m^{2}-n^{2}\right).

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

Combine like terms in m^{2}+2mn+n^{2}-m^{2}+n^{2}.

$$\frac{2n^{2}+2mn}{mn}$$

Factor the expressions that are not already factored in \frac{2n^{2}+2mn}{mn}.

$$\frac{2n\left(m+n\right)}{mn}$$

Cancel out n in both numerator and denominator.

$$\frac{2\left(m+n\right)}{m}$$

Use the distributive property to multiply 2 by m+n.

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