Solve m^2+1/m^2+2-2m-2/m

$$m ^ { 2 } + \frac { 1 } { m ^ { 2 } } + 2 - 2 m - \frac { 2 } { m }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m^{2}+2-2m times \frac{m^{2}}{m^{2}}.

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

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

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

Do the multiplications in \left(m^{2}+2-2m\right)m^{2}+1.

$$\frac{m^{4}+2m^{2}-2m^{3}+1}{m^{2}}-\frac{2}{m}$$

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

$$\frac{m^{4}+2m^{2}-2m^{3}+1}{m^{2}}-\frac{2m}{m^{2}}$$

Since \frac{m^{4}+2m^{2}-2m^{3}+1}{m^{2}} and \frac{2m}{m^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{m^{4}+2m^{2}-2m^{3}+1-2m}{m^{2}}$$

Factor

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