Solve =-m/2+n/2+2-m^2/2+5/2m-2

$$= - \frac { m } { 2 } + \frac { n } { 2 } + 2 - \frac { m ^ { 2 } } { 2 } + \frac { 5 } { 2 } m - 2$$

Evaluate

$$\frac{n+4m-m^{2}}{2}$$

Short Solution Steps

Combine -\frac{m}{2} and \frac{5}{2}m to get 2m.

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

Subtract 2 from 2 to get 0.

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

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

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

Since \frac{2\times 2m}{2} and \frac{n}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 2m+n.

$$\frac{4m+n}{2}-\frac{m^{2}}{2}$$

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

$$\frac{4m+n-m^{2}}{2}$$

Factor

$$\frac{n+4m-m^{2}}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{4m+n-m^{2}}{2}$$