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## Homework Statement

I was solving a problem and came to a part where I was dealing with the expression,

1 - e

^{-t}

--------

1 - e

^{t}

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!

## Homework Equations

N/A

## The Attempt at a Solution

N/A[/B]