The expression provided is:

$\frac{3 - x^3}{\sqrt{x}}$

To simplify this expression, follow these steps:

1. Separate the terms in the numerator: You can write the expression as:

$\frac{3 - x^3}{\sqrt{x}} = \frac{3}{\sqrt{x}} - \frac{x^3}{\sqrt{x}}$

2. Simplify each term:

   • The first term can be simplified as: $\frac{3}{\sqrt{x}} = 3x^{-\frac{1}{2}}$
   • The second term involves dividing $x^3$ by $\sqrt{x}$, which can be simplified as: $\frac{x^3}{\sqrt{x}} = x^3 \cdot x^{-\frac{1}{2}} = x^{3 - \frac{1}{2}} = x^{\frac{5}{2}}$

3. Combine the simplified terms: $\frac{3 - x^3}{\sqrt{x}} = 3x^{-\frac{1}{2}} - x^{\frac{5}{2}}$

Thus, the fully simplified form of the given expression is:

$3x^{-\frac{1}{2}} - x^{\frac{5}{2}}$

Would you like more details on any step? Here are some questions to expand your understanding:

1. How do you simplify a term with a negative exponent?
2. What is the general rule for dividing powers with the same base?
3. How does the property $a^m \times a^n = a^{m+n}$ apply in this simplification?
4. How would you express $x^{-\frac{1}{2}}$ in radical form?
5. Can this expression be factored further?

Tip: When simplifying expressions with exponents, remember to handle each term individually and combine them carefully according to the rules of exponents.