Solve m(m+n)/(m-1)^2*m-1/mn+m^2

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

Evaluate

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

Short Solution Steps

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

$$\frac{m^{2}+mn}{\left(m-1\right)^{2}}\times \frac{m-1}{mn+m^{2}}$$

Multiply \frac{m^{2}+mn}{\left(m-1\right)^{2}} times \frac{m-1}{mn+m^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m^{2}+mn\right)\left(m-1\right)}{\left(m-1\right)^{2}\left(mn+m^{2}\right)}$$

Cancel out \left(m-1\right)\left(m^{2}+mn\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{m^{2}+mn}{\left(m-1\right)^{2}}\times \frac{m-1}{mn+m^{2}}$$

Multiply \frac{m^{2}+mn}{\left(m-1\right)^{2}} times \frac{m-1}{mn+m^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m^{2}+mn\right)\left(m-1\right)}{\left(m-1\right)^{2}\left(mn+m^{2}\right)}$$

Cancel out \left(m-1\right)\left(m^{2}+mn\right) in both numerator and denominator.

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