Strategies for Simplifying Fractions with Exponential Terms

[Andrusko]

Fraction is:

$$\frac{1-e^{-x}}{1-e^{x}}$$

and it's meant to go to:

$$-e^{-x}$$

I can't make it look like it needs to. I tried splitting it up but that goes nowhere.

What other strategies are there for simplifying fractions like this?

Thanks for any help.

 

[Borek]

$$1-e^{-x} = -e^{-x}(...)$$

 

[Andrusko]

$$1 - e^{-x} = -e^{-x} + 1$$

? Still don't get it sorry...

 

[Borek]

$$1-e^{-x} = -e^{-x}(... - 1)$$

 

[gabbagabbahey]

What do you get when you multiply both the numerator and the denominator by $-e^{-x}$?

 

[HallsofIvy]

Or multiply numerator and denominator by the "conjugate", 1+ e^-x.