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 \(\frac {m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m-n\).
\[\] Notations:
- \( \lfloor \cdot \rfloor \) denotes the floor function.
- \( \{ \cdot \} \) denotes the fractional part function.
by
Md Zuhair