1. **State the problem:** Simplify the expression $$\frac{\sqrt{24x^3}}{\sqrt{3x^2}} - \sqrt{50x}$$. 2. **Use the property of radicals:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$ and $$\sqrt{a} - \sqrt{b}$$ remains as is until simplified. 3. Simplify the first term: $$\frac{\sqrt{24x^3}}{\sqrt{3x^2}} = \sqrt{\frac{24x^3}{3x^2}} = \sqrt{8x}$$. 4. Simplify the second term: $$\sqrt{50x}$$. 5. Factor inside the radicals: $$\sqrt{8x} = \sqrt{4 \cdot 2 \cdot x} = \sqrt{4} \cdot \sqrt{2x} = 2\sqrt{2x}$$ $$\sqrt{50x} = \sqrt{25 \cdot 2 \cdot x} = \sqrt{25} \cdot \sqrt{2x} = 5\sqrt{2x}$$ 6. Substitute back: $$2\sqrt{2x} - 5\sqrt{2x} = (2 - 5)\sqrt{2x} = -3\sqrt{2x}$$ 7. **Final answer:** $$-3\sqrt{2x}$$. This matches the option **-3√(2x)**. **Explanation:** We used properties of radicals to combine and simplify the terms step-by-step, factoring perfect squares out of the radicals to simplify them fully.