[D] Poles of non-linear rational features

Suppose I want to fit a linear model to non-linear rational features. Something like RationalTransformer instead of SplineTransformer in Scikit-Learn, that uses a basis of rational functions. The domain of my raw features before being transformed are (theoretically) unbounded non-negative numbers, such as "time since X happened", "total time spent on the website", or "bid in an auction".

So here is the question: where would you put the poles? Why?

Note, I'm not aiming on fitting one rational curve, so algorithms in the spirit of AAA are irrelevant. I'm aiming at a component I can use in a pipeline that transformes features before model fitting, such as MinMaxScaler or SplineTransformer in scikit-learn.