Question: how to simplify this : help please

we have the following:

CM := MultiSeries:-series((c[1]*e+c[2]*e^2+c[3]*e^3+c[4]*e^4+O(e^5))^m, e)

CM := c[1]^m*e^m+c[2]*m*c[1]^m*e^(1+m)/c[1]+(1/2)*m*(2*c[3]*c[1]+c[2]^2*m-c[2]^2)*c[1]^m*e^(2+m)/c[1]^2+(1/6)*m*(6*c[4]*c[1]^2+6*c[3]*c[2]*c[1]*m-6*c[3]*c[2]*c[1]+c[2]^3*m^2-3*c[2]^3*m+2*c[2]^3)*c[1]^m*e^(3+m)/c[1]^3+O(e^(4+m))

A := c[1]*e+c[2]*e^2+c[3]*e^3+c[4]*e^4+O(e^5)

dA := diff(A, e)

dA := c[1]+2*c[2]*e+3*c[3]*e^2+4*c[4]*e^3+O(e^4)

Now how to simplify the following expression:

(k1*A)/(k2*dA + CM*k3*k4)

here k1, k2, k3, k4 are numbers

we may further assume m > 0

 if we try:

series ((k1*A)/(k2*dA + CM*k3*k4),e)

it complains about sign of exponent

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