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For two lists of non-zero real numbers $a_i$ and $b_i$, $i=1,...,N$, how to express $x$, in terms of the $a_i$'s and $b_i$'s, such that $\sum_{i=1,...,N}\frac{a_i}{b_i+x}=1$?

Thank you.

Smile
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  • Have a look at https://math.stackexchange.com/questions/3078167/efficient-algorithm-for-solving-equation-sum-n-a-n-x-x-n-1/3079024#3079024 – Claude Leibovici Nov 12 '19 at 09:22
  • Thanks! But in addition to numerical solutions, I still wish to see if there exist some analytical closed form solution. – Smile Nov 13 '19 at 04:11
  • You can transform the equation to a polynomial and solve it. The problem is that is feasible if $N \leq 4$. – Claude Leibovici Nov 13 '19 at 05:45

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