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Define $f(x)=\frac{x^2+12x+18}{x^2-8x-2}$, find the value of $\frac{7}{306 \sqrt{\displaystyle 14 \left (\prod_{x=1}^{100}{f(x)} \right) \left(\prod_{n=97}^{106}{\frac{1}{n^2-18}}\right)}}$

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