Solve 5m+5n/m^2-n^2*m^2-mn/(m+n)^2

$$\frac { 5 m + 5 n } { m ^ { 2 } - n ^ { 2 } } \cdot \frac { m ^ { 2 } - m n } { ( m + n ) ^ { 2 } }$$

Evaluate

$$\frac{5m}{\left(m+n\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5m+5n}{m^{2}-n^{2}}.

$$\frac{5\left(m+n\right)}{\left(m+n\right)\left(m-n\right)}\times \frac{m^{2}-mn}{\left(m+n\right)^{2}}$$

Cancel out m+n in both numerator and denominator.

$$\frac{5}{m-n}\times \frac{m^{2}-mn}{\left(m+n\right)^{2}}$$

Multiply \frac{5}{m-n} times \frac{m^{2}-mn}{\left(m+n\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(m^{2}-mn\right)}{\left(m-n\right)\left(m+n\right)^{2}}$$

Factor the expressions that are not already factored.

$$\frac{5m\left(m-n\right)}{\left(m-n\right)\left(m+n\right)^{2}}$$

Cancel out m-n in both numerator and denominator.

$$\frac{5m}{\left(m+n\right)^{2}}$$

Expand the expression.

$$\frac{5m}{m^{2}+2mn+n^{2}}$$

Expand

$$\frac{5m}{\left(m+n\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5m+5n}{m^{2}-n^{2}}.

$$\frac{5\left(m+n\right)}{\left(m+n\right)\left(m-n\right)}\times \frac{m^{2}-mn}{\left(m+n\right)^{2}}$$

Cancel out m+n in both numerator and denominator.

$$\frac{5}{m-n}\times \frac{m^{2}-mn}{\left(m+n\right)^{2}}$$

Multiply \frac{5}{m-n} times \frac{m^{2}-mn}{\left(m+n\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(m^{2}-mn\right)}{\left(m-n\right)\left(m+n\right)^{2}}$$

Factor the expressions that are not already factored.

$$\frac{5m\left(m-n\right)}{\left(m-n\right)\left(m+n\right)^{2}}$$

Cancel out m-n in both numerator and denominator.

$$\frac{5m}{\left(m+n\right)^{2}}$$

Expand the expression.

$$\frac{5m}{m^{2}+2mn+n^{2}}$$