We are asked to add the two algebraic fractions $\frac{n}{5}$ and $\frac{8n}{15}$ and simplify the result.

1. Problem Description

We are asked to add the two algebraic fractions $\frac{n}{5}$ and $\frac{8n}{15}$ and simplify the result.

2. Solution Steps

To add the two fractions, we need to find a common denominator. The least common multiple of 5 and 15 is

1

5.

We rewrite the first fraction with the denominator 15:

$\frac{n}{5} = \frac{n \times 3}{5 \times 3} = \frac{3n}{15}$.

Now, we can add the two fractions:

$\frac{3n}{15} + \frac{8n}{15} = \frac{3n + 8n}{15} = \frac{11n}{15}$.

The fraction $\frac{11n}{15}$ is in its simplest form because 11 and 15 have no common factors other than

1.

3. Final Answer

$\frac{11n}{15}$