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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.

Learn how to simplify the expression (3 - x^3) / sqrt(x) with detailed step-by-step instructions. This problem involves exponents and fractional exponents, covering key algebraic concepts. Suitable for students in Grades 9-12.

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