Solve n^2+7n+10/n+1+n^2-3n/n+1

$$\frac { n ^ { 2 } + 7 n + 10 } { n + 1 } + \frac { n ^ { 2 } - 3 n } { n + 1 }$$

Evaluate

$$\frac{2\left(n^{2}+2n+5\right)}{n+1}$$

Short Solution Steps

Since \frac{n^{2}+7n+10}{n+1} and \frac{n^{2}-3n}{n+1} have the same denominator, add them by adding their numerators.

$$\frac{n^{2}+7n+10+n^{2}-3n}{n+1}$$

Combine like terms in n^{2}+7n+10+n^{2}-3n.

$$\frac{2n^{2}+4n+10}{n+1}$$

Expand

$$\frac{2\left(n^{2}+2n+5\right)}{n+1}$$

Short Solution Steps

Since \frac{n^{2}+7n+10}{n+1} and \frac{n^{2}-3n}{n+1} have the same denominator, add them by adding their numerators.

$$\frac{n^{2}+7n+10+n^{2}-3n}{n+1}$$

Combine like terms in n^{2}+7n+10+n^{2}-3n.

$$\frac{2n^{2}+4n+10}{n+1}$$