What is the value of
$\sum_{x\in\mathbb{Q}\setminus\{0\}, |x|<1}(\mathrm{denominator}\;\; \mathrm{of}\;\; x)^{-2}?$
(the denominator of a nonzero rational number $x$ is defined to be $b$ where $x=a/b$ with $a\in\mathbb{Z}\setminus\{0\}$, $b\in\mathbb{N}_{>0}$, and $a,b$ are relatively prime).
Or, is there a "nice" expression for the above sum?
Edit: Forgot to write a hypothesis. I'm considering only those rationals with $|x|<1$.