# Rearrangement of matrix inverse sum expression

Mathematics Asked on January 1, 2022

I have an expression of the below form:

$$sum_{i=1}^k (A_i+B)^{-1}=0$$
where $${A_i}_{iin {1,…k}}$$ are a set of known square symmetric invertible matrices and $$B$$ is an unknown square symmetric invertible matrix.

I wish to rearrange the above for $$B$$. How can I do this? It seems as though there must be a simple way but I cannot see one.

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