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

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

Evaluate

$$\frac{\left(m+1\right)\left(m+4\right)}{2\left(m+2\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}+2m+1}{2m+2}.

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

Cancel out m+1 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m+2}{m+2}.

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

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

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

Combine like terms in m+2-1.

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

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

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

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

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

Do the multiplications in 2\left(m+1\right)+\left(m+1\right)\left(m+2\right).

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

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

$$\frac{5m+4+m^{2}}{2\left(m+2\right)}$$

Expand 2\left(m+2\right).

$$\frac{5m+4+m^{2}}{2m+4}$$

Expand

$$\frac{m^{2}+5m+4}{2\left(m+2\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}+2m+1}{2m+2}.

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

Cancel out m+1 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m+2}{m+2}.

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

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

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

Combine like terms in m+2-1.

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

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

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

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

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

Do the multiplications in 2\left(m+1\right)+\left(m+1\right)\left(m+2\right).

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

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

$$\frac{5m+4+m^{2}}{2\left(m+2\right)}$$

Expand 2\left(m+2\right).

$$\frac{5m+4+m^{2}}{2m+4}$$