Solve m+2/2-m/m+2+2m^2-m^3/2m^2-8

$$\frac { m + 2 } { 2 } - \frac { m } { m + 2 } + \frac { 2 m ^ { 2 } - m ^ { 3 } } { 2 m ^ { 2 } - 8 }$$

Evaluate

$$1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2m^{2}-m^{3}}{2m^{2}-8}.

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

Extract the negative sign in 2-m.

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

Cancel out m-2 in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

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

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

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

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

Do the multiplications in \left(m+2\right)\left(m+2\right)-2m.

$$\frac{m^{2}+2m+2m+4-2m}{2\left(m+2\right)}+\frac{m^{2}}{-2\left(m+2\right)}$$

Combine like terms in m^{2}+2m+2m+4-2m.

$$\frac{m^{2}+2m+4}{2\left(m+2\right)}+\frac{m^{2}}{-2\left(m+2\right)}$$

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

$$\frac{m^{2}+2m+4}{2\left(m+2\right)}+\frac{-m^{2}}{2\left(m+2\right)}$$

Since \frac{m^{2}+2m+4}{2\left(m+2\right)} and \frac{-m^{2}}{2\left(m+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{m^{2}+2m+4-m^{2}}{2\left(m+2\right)}$$

Combine like terms in m^{2}+2m+4-m^{2}.

$$\frac{2m+4}{2\left(m+2\right)}$$

Factor the expressions that are not already factored in \frac{2m+4}{2\left(m+2\right)}.

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

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

$$1$$

Factor

$$1$$