Quick question about simplifying a differential equation?

[MathWarrior]

I have solved this equation but I am just not quite sure why this final result is the way it is.

\frac{2e^{t}+C}{e^{t}} = 2e^{-t} + C

Why is it e^{-t} when its simplified ?

 

[wukunlin]

uhhh, how did you get that?

shouldn't it be...
\frac{2e^{t}+C}{e^{t}}
= 2 \frac{ e^{t} }{ e^{t} } + \frac{ C }{ e^{t} }
= 2 + C e^{-t}

 

[encorelui2]

I also got e^(-t) = -1