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The given problem asks for the value of \( k \), a positive constant, in the expansion of:

\[
(kx + \frac{1}{x})^5 + (1 - \frac{2}{x})^8
\]
where the coefficient of \( \frac{1}{x} \) in this expansion is 74.

### Solution:

We need to find the terms in the binomial expansions of \( (kx + \frac{1}{x})^5 \) and \( (1 - \frac{2}{x})^8

The coefficient of \( \frac{1}{x} \) in the expansion of \( (kx + \frac{1}{x})^5 + (1 - \frac{2}{x})^8 \) is 74. Find the value of the positive constant \( k \).

Solve a binomial expansion problem where the coefficient of \( \frac{1}{x} \) in the expansion of \( (kx + \frac{1}{x})^5 + (1 - \frac{2}{x})^8 \) is 74. This problem requires understanding binomial expansions and identifying specific terms to find the constant \( k \). Suitable for advanced high school students.

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