# Solve this floor function

Algebra Level 4

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

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

 Notations:

×