Solve k/k+1+k+1/k+1left(k+2right)

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

Evaluate

$$\frac{3k+1}{2\left(k+1\right)}$$

Short Solution Steps

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

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

Cancel out k+1 in both numerator and denominator.

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

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

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

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

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

Combine like terms in 2k+k+1.

$$\frac{3k+1}{2\left(k+1\right)}$$

Expand 2\left(k+1\right).

$$\frac{3k+1}{2k+2}$$

Expand

$$\frac{3k+1}{2\left(k+1\right)}$$

Short Solution Steps

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

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

Cancel out k+1 in both numerator and denominator.

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

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

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

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

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

Combine like terms in 2k+k+1.

$$\frac{3k+1}{2\left(k+1\right)}$$

Expand 2\left(k+1\right).

$$\frac{3k+1}{2k+2}$$