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