Effective way to calculate the inverse (A+kB)^-1 with k changing and A, B fixed

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I have a Simulink modell where I need to calculate $(A+c_k B)^{-1}$ in every time step with $c_k$ changing each iteration. Does someone know any more effective way to do it, instead of calculating a completely new inverse in every step? Thank you!

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@ Alex B. , specify the considered matrices $A,B$. If $B$ has a small rank, then one can do something for you, otherwise not.

More precisely, if $rank(B)=r$, then, using the Sherman-Morrison formula, we obtain the required inverse with complexity $\sim 3n^2r$ multiplications. That is interesting iff $r<n/3$.