(i) To find the first 3 terms in the expansion of \(\left( 2x - \frac{3}{x} \right)^5\), we use the binomial theorem:

\(\left( 2x - \frac{3}{x} \right)^5 = \sum_{k=0}^{5} \binom{5}{k} (2x)^{5-k} \left(-\frac{3}{x}\right)^k\).

The first three terms are:

For \(k=0\): \(\binom{5}{0} (2x)^5 \left(-\frac{3}{x}\right)^0 = 32x^5\).

For \(k=1\): \(\binom{5}{1} (2x)^4 \left(-\frac{3}{x}\right)^1 = -240x^3\).

For \(k=2\): \(\binom{5}{2} (2x)^3 \left(-\frac{3}{x}\right)^2 = 720x\).

Thus, the first three terms are \(32x^5 - 240x^3 + 720x\).

(ii) To find the coefficient of \(x\) in the expansion of \(\left( 1 + \frac{2}{x^2} \right) \left( 2x - \frac{3}{x} \right)^5\), we multiply the first three terms of the expansion by \(1 + \frac{2}{x^2}\):

\((1 + \frac{2}{x^2})(32x^5 - 240x^3 + 720x)\).

The coefficient of \(x\) comes from:

\(1 \times 720x = 720x\) and \(\frac{2}{x^2} \times (-240x^3) = -480x\).

Adding these gives \(720 - 480 = 240\).

Thus, the coefficient of \(x\) is 240.