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not eliminating parameter


Eliminate[ { x /c == Coth[x/c], y/c ==  Cosh[x/c]}, c ]

It was expected with the first relation that x/c would be iterated in
a FindRoot / NSolve mode to get a solution, say x/c = u, c = x/u
leading to y/x = Cosh[u]/u by insertion into the second equation.

But but there are no solutions, several &&s appear. I could have done
the first one manually, but is   there some automatic way out?

Thanks for indication.

Narasimham


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