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The problem asks to calculate the limit:

\[
\lim_{x \to 0} \left[\frac{\left(\frac{2}{x} + 3\right)}{\left(\frac{3}{x} - 1\right)}\right]
\]

### Step-by-step solution:

1. **Analyze the behavior as \( x \to 0 \):**
   - The term \( \frac{2}{x} \) grows large as \( x \to 0 \) (tends towards \( \infty \) or \( -\infty \) depending on the direction of approach).
   - Similarly, \( \frac{3}{x} \) grows large as \( x \to 0 \).

2. **Factor out \( \frac{1}{x} \) from both the numerator and denominator:**

   In the numerator, we have:
   \[
   \frac{2}{x} + 3 = \frac{1}{x} (2 + 3x)
   \]
   
   In the denominator:
   \[
   \frac{3}{x} - 1 = \frac{1}{x} (3 - x)
   \

Learn how to solve the limit lim x→0 [(2/x + 3) / (3/x - 1)] with a detailed step-by-step explanation. This problem involves key concepts of limits and algebraic simplification. Suitable for advanced mathematics students in Grades 11-12.

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