how is it possible to divide tow equations with Mathematica?

I have the following code:

eqn416 = a == Kp h (1 - E^(-ta/tau))
eqn417 = a/2 == Kp h (1 - E^(-ta2/tau))

Obviously one will get

2 E^(-(ta2/tau)) - E^(-(ta/tau)) == 1

by dividing them, but with

Eliminate[{eqn416, eqn417}, {Kp, h, a}]

I only get 'True'.

And if I try just to eliminate 2 of them and assuming afterwards 'a' is not zero

Eliminate[{eqn416, eqn417}, {Kp, h}];
%[[2]]
FullSimplify[%, a != 0]

I'm not getting rid of 'a'!

FullSimplify[a (1 + E^(-(ta/tau)) - 2 E^(-(ta2/tau))) == 0, 
 a != 0]
(* Out[434]= a (1 + E^(-(ta/tau)) - 2 E^(-(ta2/tau))) == 0 *)

Any suggestions?

how is it possible to divide two equations with Mathematica?

I have the following code:

eqn416 = a == Kp h (1 - E^(-ta/tau))
eqn417 = a/2 == Kp h (1 - E^(-ta2/tau))

Obviously one will get

2 E^(-(ta2/tau)) - E^(-(ta/tau)) == 1

by dividing them, but with

Eliminate[{eqn416, eqn417}, {Kp, h, a}]

I only get 'True'.

And if I try just to eliminate 2 of them and assuming afterwards 'a' is not zero

Eliminate[{eqn416, eqn417}, {Kp, h}];
%[[2]]
FullSimplify[%, a != 0]

I'm not getting rid of 'a'!

FullSimplify[a (1 + E^(-(ta/tau)) - 2 E^(-(ta2/tau))) == 0, 
 a != 0]
(* Out[434]= a (1 + E^(-(ta/tau)) - 2 E^(-(ta2/tau))) == 0 *)

Any suggestions?

how is it possible to divide tow equations with Mathematica?

I have the following code:

eqn416 = a == Kp h (1 - E^(-ta/tau))
eqn417 = a/2 == Kp h (1 - E^(-ta2/tau))

Obviously one will get

2 E^(-(ta2/tau)) - E^(-(ta/tau)) == 1

by dividing them, but with

Eliminate[{eqn416, eqn417}, {Kp, h, a}]

I only get 'True'.

And if I try just to eliminate 2 of them and assuming afterwards 'a' is not zero

Eliminate[{eqn416, eqn417}, {Kp, h}];
%[[2]]
FullSimplify[%, a != 0]

I'm not getting rid of 'a'!

Any suggestions?

how is it possible to divide tow equations with Mathematica?

I have the following code:

eqn416 = a == Kp h (1 - E^(-ta/tau))
eqn417 = a/2 == Kp h (1 - E^(-ta2/tau))

Obviously one will get

2 E^(-(ta2/tau)) - E^(-(ta/tau)) == 1

by dividing them, but with

Eliminate[{eqn416, eqn417}, {Kp, h, a}]

I only get 'True'.

And if I try just to eliminate 2 of them and assuming afterwards 'a' is not zero

Eliminate[{eqn416, eqn417}, {Kp, h}];
%[[2]]
FullSimplify[%, a != 0]

I'm not getting rid of 'a'!

FullSimplify[a (1 + E^(-(ta/tau)) - 2 E^(-(ta2/tau))) == 0, 
 a != 0]
(* Out[434]= a (1 + E^(-(ta/tau)) - 2 E^(-(ta2/tau))) == 0 *)

Any suggestions?