Add. Assume that all variables represent positive real numbers. \( \frac{\sqrt{75 x}}{6}+\sqrt{\frac{3 x}{9}} \) \( \frac{\sqrt{75 x}}{6}+\sqrt{\frac{3 x}{9}}=\square \) (Type an exact answer, using radicals as needed. Simplify your answer.)

Let's simplify the expression step by step. First, rewrite \( \sqrt{\frac{3x}{9}} \): \[ \sqrt{\frac{3x}{9}} = \sqrt{\frac{3x}{3^2}} = \frac{\sqrt{3x}}{3} \] Now we can rewrite the entire expression: \[ \frac{\sqrt{75x}}{6} + \frac{\sqrt{3x}}{3} \] Next, simplify \( \sqrt{75x} \): \[ \sqrt{75x} = \sqrt{75} \cdot \sqrt{x} = \sqrt{25 \cdot 3} \cdot \sqrt{x} = 5\sqrt{3x} \] Substituting this back into our expression gives: \[ \frac{5\sqrt{3x}}{6} + \frac{\sqrt{3x}}{3} \] Now, we'll rewrite \( \frac{\sqrt{3x}}{3} \) with a common denominator of 6: \[ \frac{\sqrt{3x}}{3} = \frac{2\sqrt{3x}}{6} \] Now, combine the two fractions: \[ \frac{5\sqrt{3x}}{6} + \frac{2\sqrt{3x}}{6} = \frac{(5 + 2)\sqrt{3x}}{6} = \frac{7\sqrt{3x}}{6} \] Thus, the exact answer, simplified, is: \[ \frac{7\sqrt{3x}}{6} \]