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### Compute roots of sum_i c_i/(a_i + b_i x)^p

How to compute the (real) roots of
$$\sum_{i=1}^n \frac{c_i}{(a_i + b_i \cdot x)^p}$$
for given reals $a_i, b_i, c_i$, and positive integers $n, p$? The cases $p=1, ..., 5$ and $n=6, ..., 20$ would ...