Solve =n/(n+1)+1/(n+1)(n+2)

$$= \frac { n } { ( n + 1 ) } + \frac { 1 } { ( n + 1 ) ( n + 2 ) }$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Cancel out n+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

Cancel out n+1 in both numerator and denominator.

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