I have many expressions of the form $c_1/\epsilon, c_2/\epsilon \dots ,c_n/\epsilon$ where $n$ is a large number and I also have expressions of the form $b_1\epsilon, b_2\epsilon, \dots ,b_m \epsilon$ where $m$ is also very large. $c_i$ and $b_i$ are just $\epsilon$-independent variables or numbers.
I would like to put the terms in which $\epsilon$ appears in the numerator to zero without affecting the terms in which $\epsilon$ appears in the denominator. Is there a way to automate this in Mathematica? Probably the answer is yes and the solution is very simple but I have not found the correct syntax yet.
gives rise to errors because of producing indeterminate forms, as expected.