Can't simplify this fraction

1. Oct 6, 2008

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.

2. Oct 6, 2008

Staff: Mentor

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

3. Oct 6, 2008

Andrusko

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

? Still don't get it sorry...

4. Oct 6, 2008

Staff: Mentor

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

5. Oct 6, 2008

gabbagabbahey

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

6. Oct 6, 2008

HallsofIvy

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