Solve for x: $\frac{a_1}{x^{-a_1}-1} + \dots + \frac{a_n}{x^{-a_n}-1} = b$

Question

I'm trying to solve this equation for $x$ :

\begin{equation} \frac{a_1}{x^{-a_1}-1} + \dots + \frac{a_n}{x^{-a_n}-1} = b \end{equation} where $b$ and $a_i$'s are positive integers.

I'm not sure whether it is possible to solve this equation. Any hints or tips are appreciated. Thanks in advance.