Recurring Styles #3 - A Twisted Recurrence!

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

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 $\large{{\left\lfloor \frac{x_{10}}{x_{20}} \right\rfloor}}$ .