1. **State the problem:** Simplify the expression $$\frac{5}{\sqrt{x}+3}$$ and relate it to the expression $2x^3$ given. 2. **Recall the formula and rules:** To simplify a fraction with a radical in the denominator, multiply numerator and denominator by the conjugate of the denominator to rationalize it. 3. **Apply rationalization:** Multiply numerator and denominator by $\sqrt{x}-3$: $$\frac{5}{\sqrt{x}+3} \times \frac{\sqrt{x}-3}{\sqrt{x}-3} = \frac{5(\sqrt{x}-3)}{(\sqrt{x}+3)(\sqrt{x}-3)}$$ 4. **Simplify the denominator using difference of squares:** $$(\sqrt{x}+3)(\sqrt{x}-3) = (\sqrt{x})^2 - 3^2 = x - 9$$ 5. **Write the simplified expression:** $$\frac{5(\sqrt{x}-3)}{x-9} = \frac{5\sqrt{x} - 15}{x-9}$$ 6. **Interpret the expression $2x^3$:** This is a separate expression and does not simplify with the fraction above unless specified. **Final simplified form:** $$\frac{5\sqrt{x} - 15}{x-9}$$