Solve 2/n+8+4/n+1

$$\frac { 2 } { n + 8 } + \frac { 4 } { n + 1 }$$

Evaluate

$$\frac{2\left(3n+17\right)}{\left(n+1\right)\left(n+8\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n+8 and n+1 is \left(n+1\right)\left(n+8\right). Multiply \frac{2}{n+8} times \frac{n+1}{n+1}. Multiply \frac{4}{n+1} times \frac{n+8}{n+8}.

$$\frac{2\left(n+1\right)}{\left(n+1\right)\left(n+8\right)}+\frac{4\left(n+8\right)}{\left(n+1\right)\left(n+8\right)}$$

Since \frac{2\left(n+1\right)}{\left(n+1\right)\left(n+8\right)} and \frac{4\left(n+8\right)}{\left(n+1\right)\left(n+8\right)} have the same denominator, add them by adding their numerators.

$$\frac{2\left(n+1\right)+4\left(n+8\right)}{\left(n+1\right)\left(n+8\right)}$$

Do the multiplications in 2\left(n+1\right)+4\left(n+8\right).

$$\frac{2n+2+4n+32}{\left(n+1\right)\left(n+8\right)}$$

Combine like terms in 2n+2+4n+32.

$$\frac{6n+34}{\left(n+1\right)\left(n+8\right)}$$

Expand \left(n+1\right)\left(n+8\right).

$$\frac{6n+34}{n^{2}+9n+8}$$

Factor

$$\frac{2\left(3n+17\right)}{\left(n+1\right)\left(n+8\right)}$$