\[\large{x_{n+2} = \dfrac{x_nx_{n+1}}{5x_n - 4x_{n+1}}}\]

with \(x_0 = 2; x_1 = 3\).

Let \((x_n)_{n=0}^\infty\) be a sequence that satisfies the above recurrence relation. Then find the value of \(\large{{\left\lfloor \frac{x_{10}}{x_{20}} \right\rfloor}}\).

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