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The given expression \( \frac{2}{x+3} - \frac{x}{2} \) simplifies to:

\[
\frac{-x(x + 3) + 4}{2(x + 3)} = \frac{-x^2 - 3x + 4}{2(x + 3)}
\]

Now, comparing this result with the provided answer choices:

- Option **C**: \( \frac{-x^2 + 3x + 4}{2x + 6} \)
- Option **D**: \( \frac{-x^2 - 3x + 4}{2x + 6} \)

Both options C and D have the denominator \( 2x + 6 \), which is equivalent to \( 2(x + 3) \). Since the numerator in Option **D** matches exactly with \( -x^2 - 3x + 4 \), **Option D** is the correct answer.

Would you like further details or have any questions?

Here are some related questions to explore:
1. How do you find the common denominator when subtracting fractions?
2. What are some techniques for simplifying algebraic expressions?
3. Why does factoring help in comparing algebraic expressions?
4. How can you check if two algebraic fractions are equivalent?
5. How do quadratic terms influence the behavior of algebraic fractions?

**Tip:** Always simplify the expression first before comparing it with the options provided in multiple-choice questions.

Which expression is equal to (2/(x+3)) - (x/2)?

This problem focuses on simplifying the expression (2/(x+3)) - (x/2) by finding a common denominator and comparing the results. Learn the step-by-step process of fraction subtraction and algebraic simplification. Suitable for high school students.

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