Solve frac{n^{3}-m^{3}}{n^{2}-m^{2}}*n^2+2nm+m^2/n^2+nm+m^2

$$\frac { n ^ { 3 } - m ^ { 3 } } { n ^ { 2 } - m ^ { 2 } } \cdot \frac { n ^ { 2 } + 2 n m + m ^ { 2 } } { n ^ { 2 } + n m + m ^ { 2 } }$$

Evaluate

$$m+n$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{n^{3}-m^{3}}{n^{2}-m^{2}}.

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

Cancel out -m+n in both numerator and denominator.

$$\frac{m^{2}+mn+n^{2}}{m+n}\times \frac{n^{2}+2nm+m^{2}}{n^{2}+nm+m^{2}}$$

Multiply \frac{m^{2}+mn+n^{2}}{m+n} times \frac{n^{2}+2nm+m^{2}}{n^{2}+nm+m^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m^{2}+mn+n^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out m+n in both numerator and denominator.

$$m+n$$

Expand

$$m+n$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{n^{3}-m^{3}}{n^{2}-m^{2}}.

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

Cancel out -m+n in both numerator and denominator.

$$\frac{m^{2}+mn+n^{2}}{m+n}\times \frac{n^{2}+2nm+m^{2}}{n^{2}+nm+m^{2}}$$

Multiply \frac{m^{2}+mn+n^{2}}{m+n} times \frac{n^{2}+2nm+m^{2}}{n^{2}+nm+m^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m^{2}+mn+n^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out m+n in both numerator and denominator.

$$m+n$$