problem: What is the sum of all possible solutions of $\frac{9x}{13}+\frac{13}{9x}=\frac{250}{117x}$?
solution: Knowing that $117 = 9 \times 13$, we immediately reduce the problem to finding the sum of all possible solutions of $81x^2 + 169 - 250 = 0$. Seeing that this is a quadratic whose linear coefficient is 0, the solutions sum to $\boxed{0}$.
  
  To find the solutions, we can rewrite $81x^2 -81 = 0 \implies x^2 = 1$, so the solutions are $1,-1$.