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In the expansion of (1 + (x)/(2) - (2)/(x))⁴, where x ≠ 0, what is the coefficient-free term (term independent of x)?

1. 1
2. -6
3. -5
4. 6

Correct answer: -5

Solution

The coefficient-free term in the expansion can be found by identifying the term where the powers of x cancel out. In this case, the term that results in no x dependency occurs when the contributions from rac{x}{2} and - rac{2}{x} balance each other, leading to a coefficient of -5.

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