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Step 1: Evaluate the Determinant The expression given is a determinant of a $(1 \times 3)$ matrix. To find $(e)$, evaluate the determinant by substituting $(x = 0)$. Step 2: Substitute $(x = 0)$ Substitute $(x = 0)$ in the determinant: $\left| \frac{0^3 + 3 \cdot 0}{0+1} \quad \frac{0-1}{-2 \cdot 0} \quad \frac{0-4}{0-3} \right| = \left| 0 \quad 0 \quad \frac{4}{3} \right|$ Step 3: Simplify The determinant simplifies to $(0)$ since it is a $(1 \times 3)$ matrix with two zeros. Conclusion Therefore, $(e = 0)$.

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