Simplify by rationalizing the denominator: 1. \( \frac{3-3 \sqrt{3 a}}{4 \sqrt{8 a}} \)

To simplify \( \frac{3-3 \sqrt{3 a}}{4 \sqrt{8 a}} \) by rationalizing the denominator, we first simplify the denominator: 1. \( \sqrt{8a} = \sqrt{4 \cdot 2 \cdot a} = 2\sqrt{2a} \). Thus, the expression becomes: \[ \frac{3 - 3\sqrt{3a}}{4 \cdot 2\sqrt{2a}} = \frac{3 - 3\sqrt{3a}}{8\sqrt{2a}} \] Now, to rationalize the denominator, we multiply both the numerator and denominator by \( \sqrt{2a} \): \[ \frac{(3 - 3\sqrt{3a})\sqrt{2a}}{8\sqrt{2a}\cdot\sqrt{2a}} = \frac{(3 - 3\sqrt{3a})\sqrt{2a}}{16a} \] Now, distribute in the numerator: \[ \frac{3\sqrt{2a} - 3\sqrt{6a^2}}{16a} \] Thus, the final simplified expression is: \[ \frac{3\sqrt{2a} - 3\sqrt{6a^2}}{16a} \]