1. **State the problem:** Simplify the expression $\frac{4}{x^2} - 3x$. 2. **Understand the terms:** The expression consists of two terms: $\frac{4}{x^2}$ and $-3x$. 3. **Check for common denominators:** The first term is a fraction with denominator $x^2$, the second term is a polynomial term without a denominator. 4. **Rewrite the second term with denominator $x^2$ to combine:** $$-3x = \frac{-3x \cdot x^2}{x^2} = \frac{-3x^3}{x^2}$$ 5. **Combine the terms over the common denominator $x^2$:** $$\frac{4}{x^2} - 3x = \frac{4}{x^2} + \frac{-3x^3}{x^2} = \frac{4 - 3x^3}{x^2}$$ 6. **Final simplified expression:** $$\boxed{\frac{4 - 3x^3}{x^2}}$$ This is the simplified form of the given expression, combining both terms over a common denominator.