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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in n+2+n.

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

Express \frac{2n+2}{n\left(n+2\right)}\times 2 as a single fraction.

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

Use the distributive property to multiply 2n+2 by 2.

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

Use the distributive property to multiply n by n+2.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in n+2+n.

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

Express \frac{2n+2}{n\left(n+2\right)}\times 2 as a single fraction.

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

Use the distributive property to multiply 2n+2 by 2.

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

Use the distributive property to multiply n by n+2.

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