Question: Collect terms in the denominador

I need to highlight all terms that contain eta, my variable, for example (A0)+(A1)*1/eta+(A2)*1/eta^2+...(An)**1/eta^n and so on in my expression call from P. However, when I select eta through the collect command, maple is unable to carry out the command.

P := expand((cosh(k*eta) + alpha*m*sinh(k*eta)/eta)^3);
P := convert(P, exp);
P := expand(P);
P := collect(P, eta);
P := combine(P);

Once these have are in evidence I need to select the coefficients A0, A1, A2, etc. How to proceed if eta are in the denominator and maple does not work with this possibility? This it'was my tentative

B0 := subs(eta = 0, P);

B1 := coeff(P, eta)

B2 := coeff(P, eta^2)

I actually tested the possibility of  1/eta instead of  eta and it didn't work

Please Wait...