The problem is to simplify the expression $\sqrt{320} - \sqrt{80} + \frac{\sqrt{75}}{\sqrt{9}}$.

1. Problem Description

The problem is to simplify the expression $\sqrt{320} - \sqrt{80} + \frac{\sqrt{75}}{\sqrt{9}}$.

2. Solution Steps

First, simplify each square root term individually.

$\sqrt{320} = \sqrt{64 \times 5} = \sqrt{64} \times \sqrt{5} = 8\sqrt{5}$

$\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$

$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$

$\sqrt{9} = 3$

So, $\frac{\sqrt{75}}{\sqrt{9}} = \frac{5\sqrt{3}}{3}$

Now, substitute the simplified terms back into the original expression:

$8\sqrt{5} - 4\sqrt{5} + \frac{5\sqrt{3}}{3}$

Combine the terms with $\sqrt{5}$:

$(8-4)\sqrt{5} + \frac{5\sqrt{3}}{3}$

$4\sqrt{5} + \frac{5\sqrt{3}}{3}$

3. Final Answer

The final answer is $4\sqrt{5} + \frac{5\sqrt{3}}{3}$.