Taking the limit as x approaches infinity of: can be rewritten as:
The limit as x approaches infinity of: MINUS the limit as x approaches infinity of:
But this isn't true.
If I re-arrange algebraically in the first example, I will get x=2.
However, if I solve the rewritten problem, I get infinity minus infinity or undefined...??
There is a theorem that says "IF exists and exists then .
You may be thinking that " " means that the limit exists and is infinity. That is not the case. Saying that " " means "the limit does NOT exist" (in a particular way).