Finding Coefficients

The $(r+1) \text{th}$ term of the expansion can be given by

$T_{r+1} = \dbinom 9r x^{9-r} {\left\{ \dfrac 2x \right\}}^r$

Here, we see that the exponent of $x$ is $9-2r$ .

Thus, $9-2r = 1 \implies r = 4$ .

$\therefore$ Coefficient of $x$ is $\dbinom 94 \cdot 2^4 = \boxed{2016}$ .

The expansion of $\large x$ in $(\Large x+\frac{2}{x})^{9} = x^{9}+ \frac{512}{x^{9}} + 18x^{7}+\frac{2304}{x^{7}}+144x^{5}+\frac{4608}{x^{5}}+672x^{3}+\frac{5376}{x^{3}} + \color{#3D99F6}{2016}x+ \frac{4032}{x}$