# Solve this floor function

$\large \frac 1{\lfloor x \rfloor} + \frac 1{\lfloor 2 x \rfloor} = \{ 9x \} + \frac 13$

If the smallest positive solution of $x$ satisfying the equation above is of the form $\frac {m}{n}$, where $m$ and $n$ are coprime positive integers, find $m-n$.

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