Exponential Quotient Rule

[VyseV1]

Im having some difficultly in exponential quotient rule. See when i see:

2e^x/1+e^x

I keep seeing that i can eliminate the 2e^x but it never seems to work out properly. So if anyone has tips for this that would be greatly welcomed.

 

[galactus]

\(\displaystyle \L\\\frac{(1+e^{x})(2e^{x})-(2e^{x})(e^{x})}{(1+e^{x})^{2}}\)

Factor out 2e^x and it simplifies to:

=\(\displaystyle \L\\\frac{2e^{x}}{(1+e^{x})^{2}}\)