I have this inequality:
Reduce[(4000-1000k)/(k-4) < 0]
and the answer is
k ∈ Reals
I would expect
k != 4.
The following is a kind of remedy for the problem at hand:
Even though the issues in the OP could be easily resolved nonetheless they are not mathematically correct and for this reason one could consider them as bugs, this is a similar problem
while this one is correct:
Similar issue one can find here: Issue with NSolve.
Therefore we can conclude
yield results which appear to be incorrect in special cases, they are only generically correct. All of these above work as with a simplification technique:
but from strictly mathematical point of view they shouldn't. Nevermind what the documentation says (genericity et consortes) this is of course a bug:
Please see this tutorial on the results given by symbolic functions. In short, the results returned by them are generically correct:
In version 10, one could use this workaround: