I was solving a problem and came to a part where I was dealing with the expression,
1 - e-t
1 - et
It turns out that this can be simplified to -e-t but I had no idea from simply looking at the first expression that it could be simplified, and I tried to continue using a cludgy quotient rule to get the derivative, where if I had have simplified it, it would have been much easier. Is this simply a matter of being inexperienced, or am I missing some concept in elementary algebra that would let me recognize a potential simplification? For instance, I can easily recognize difference of squares, etc, but not something like this. How can I become a stronger mathematician moving forward in this regard?
Thanks in advance!
The Attempt at a Solution