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The limit of the given expression as \( x \to \frac{1}{2} \) is approximately \( -0.2637 \).

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Here are some related questions:
1. How do we handle indeterminate forms in limits?
2. What methods can be used when direct substitution does not work in a limit?
3. How does L'Hôpital's Rule apply in limit problems like this?
4. Can you explain the behavior of rational functions near singularities?
5. What is the importance of simplifying complex fractions before evaluating limits?

**Tip:** Always check for common factors before applying direct substitution in limits to simplify the process.

lim(x→1/2) [(1 / (x - 1)) * (1 / (x + 3) - (2x / (3x + 5)))]

Find the limit of a rational expression as x approaches 1/2. This problem involves simplifying complex fractions and applying L'Hôpital's Rule to resolve indeterminate forms. Suitable for advanced high school students (Grades 11-12).

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