MathNet 2016-part-03 — 184 problems (EN–VI) Question 153

Solve, in the set of real numbers, the equation $\frac{1}{\{x\}} = \frac{1}{x} + \frac{1}{[x]}$, where $[x]$ denotes the integer part of the real number $x$, and $\{x\}$ denotes the fractional part of the real number $x$.