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

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

Evaluate

$$m-1$$

Short Solution Steps

Use the distributive property to multiply m by 1-m^{2}.

$$\frac{m-1}{m+1}-\frac{m-m^{3}}{n}\times \frac{n}{\left(m+1\right)^{2}}$$

Multiply \frac{m-m^{3}}{n} times \frac{n}{\left(m+1\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{m-1}{m+1}-\frac{\left(m-m^{3}\right)n}{n\left(m+1\right)^{2}}$$

Cancel out n in both numerator and denominator.

$$\frac{m-1}{m+1}-\frac{-m^{3}+m}{\left(m+1\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+1 and \left(m+1\right)^{2} is \left(m+1\right)^{2}. Multiply \frac{m-1}{m+1} times \frac{m+1}{m+1}.

$$\frac{\left(m-1\right)\left(m+1\right)}{\left(m+1\right)^{2}}-\frac{-m^{3}+m}{\left(m+1\right)^{2}}$$

Since \frac{\left(m-1\right)\left(m+1\right)}{\left(m+1\right)^{2}} and \frac{-m^{3}+m}{\left(m+1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(m-1\right)\left(m+1\right)-\left(-m^{3}+m\right)}{\left(m+1\right)^{2}}$$

Do the multiplications in \left(m-1\right)\left(m+1\right)-\left(-m^{3}+m\right).

$$\frac{m^{2}+m-m-1+m^{3}-m}{\left(m+1\right)^{2}}$$

Combine like terms in m^{2}+m-m-1+m^{3}-m.

$$\frac{m^{2}-m-1+m^{3}}{\left(m+1\right)^{2}}$$

Factor the expressions that are not already factored in \frac{m^{2}-m-1+m^{3}}{\left(m+1\right)^{2}}.

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

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

$$m-1$$

Expand

$$m-1$$

Short Solution Steps

Use the distributive property to multiply m by 1-m^{2}.

$$\frac{m-1}{m+1}-\frac{m-m^{3}}{n}\times \frac{n}{\left(m+1\right)^{2}}$$

Multiply \frac{m-m^{3}}{n} times \frac{n}{\left(m+1\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{m-1}{m+1}-\frac{\left(m-m^{3}\right)n}{n\left(m+1\right)^{2}}$$

Cancel out n in both numerator and denominator.

$$\frac{m-1}{m+1}-\frac{-m^{3}+m}{\left(m+1\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+1 and \left(m+1\right)^{2} is \left(m+1\right)^{2}. Multiply \frac{m-1}{m+1} times \frac{m+1}{m+1}.

$$\frac{\left(m-1\right)\left(m+1\right)}{\left(m+1\right)^{2}}-\frac{-m^{3}+m}{\left(m+1\right)^{2}}$$

Since \frac{\left(m-1\right)\left(m+1\right)}{\left(m+1\right)^{2}} and \frac{-m^{3}+m}{\left(m+1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(m-1\right)\left(m+1\right)-\left(-m^{3}+m\right)}{\left(m+1\right)^{2}}$$

Do the multiplications in \left(m-1\right)\left(m+1\right)-\left(-m^{3}+m\right).

$$\frac{m^{2}+m-m-1+m^{3}-m}{\left(m+1\right)^{2}}$$

Combine like terms in m^{2}+m-m-1+m^{3}-m.

$$\frac{m^{2}-m-1+m^{3}}{\left(m+1\right)^{2}}$$

Factor the expressions that are not already factored in \frac{m^{2}-m-1+m^{3}}{\left(m+1\right)^{2}}.

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

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

$$m-1$$