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

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

Evaluate

$$\frac{2n^{2}+4n+3}{n+1}$$

Short Solution Steps

Use the distributive property to multiply 2 by n+1.

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

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

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

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

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

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

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

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

$$\frac{2n^{2}+4n+3}{n+1}$$

Expand

$$\frac{2n^{2}+4n+3}{n+1}$$

Short Solution Steps

Use the distributive property to multiply 2 by n+1.

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

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

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

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

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

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

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

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

$$\frac{2n^{2}+4n+3}{n+1}$$