Solve n+1/2n*(1-1/(n+1)^2)=

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in \left(n+1\right)^{2}-1.

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

Combine like terms in n^{2}+2n+1-1.

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

Multiply \frac{n+1}{2n} times \frac{n^{2}+2n}{\left(n+1\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out n+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out n in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in \left(n+1\right)^{2}-1.

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

Combine like terms in n^{2}+2n+1-1.

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

Multiply \frac{n+1}{2n} times \frac{n^{2}+2n}{\left(n+1\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out n+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out n in both numerator and denominator.

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

Expand the expression.

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