Get rid of a variable using Simplify/Assuming

Questions
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1

Hey Community,

After searching the help and web, i hope you can help me:

I have the following code:

eqn416 = a == Kp h (1 - E^(-ta/\[Tau]))
eqn417 = a/2 == Kp h (1 - E^(-ta2/\[Tau]))
Eliminate[{eqn416, eqn417}, {Kp, h}]
eqn418 = Simplify[%[[2]], a != 0]

But eqn418 still contains ‘a’. How can I get rid of it?
Or how can i get rid of it just using Eliminate?

Or is there an other way do ‘divide’ eqn416 by eqn417?
The only way to ‘divide’ two equations I found was doing it by Eliminate.

Interesting fact: if I use the same code with ‘e’ instead of ‘E’, it will work.

2

Try FullSimplify.

3

Thanks for this advise. I tryed it before: With FullSimplify, I’ll get a solution which gives me the same tau as “my solution”,
but plotting these two, will result in two completely different graphs!
Since I work with a book, I would like to get the solution, the author used in his book …

4

Perhaps

asub = First @ Solve[eqn416, a]
Simplify[{eqn417} /. asub, h Kp != 0]

or

Eliminate[{eqn416, eqn417}, {a}]
eqn418 = Simplify[%[[2]], Kp h != 0]

yields the desired output.