How to realize this simplification canceling each term by a factor

Questions
,
1

eq1 = 1/(2 (-1 +
A3) A4 v0) ((-1 + 2 A3 - A4) v0 SuperStar[(Subscript[c,
m])] - (-1 + A4) (-A1 A3 + Imax +
Sqrt[(-A1 A3 + Imax)^2 +
2 (A2 A3 - Imax) v0 SuperStar[(Subscript[c, m])] +
v0^2 (SuperStar[(Subscript[c, m])])^2]))

cancel each term in eq1 with

 v0 c_m^*
2

Does this do what you want?

Simplify[eq1,v0 (SuperStar[(Subscript[c, m])])==1]

which returns

-(1 - 2*A3 + A1*A3 + A4 - A1*A3*A4 - Imax + A4*Imax + (-1 + A4)*Sqrt[2*A2*A3 +
A1^2*A3^2 + (-1 + Imax)^2 - 2*A1*A3*Imax])/(2*(-1 + A3)*A4*v0)

Or this

eq1/.{v0 (SuperStar[(Subscript[c, m])])->1,v0^2 (SuperStar[(Subscript[c, m])])^2->1}

which returns this

(-1 + 2*A3 - A4 - (-1 + A4)*(-(A1*A3) + Imax + Sqrt[1 + 2*(A2*A3 - Imax) +
(-(A1*A3) + Imax)^2]))/(2*(-1 + A3)*A4*v0)
3

This is not expected. My expectation is Canceling

 v0 c_m^*

from the numerator and the denominator of eq1.

4

I am sorry that I did not understand what you expected.

If I look at eq1 then the denominator is 2 (-1+A3) A4 v0 and that does not contain v0 c_m*

Can you show what the result should be after cancelling?

Perhaps that will help me understand.