# Math Help - differential equation (checking a simplification)

1. ## differential equation (checking a simplification)

I had a differential equation and I have also computed the general solution of the equation, but i want to check whether my simplification is right for the following

[−(e^−x)/(1 + e^x)] − [(e^−2x)/(1 + e^x)] = −e^(−2x)

Is this right...

2. Originally Posted by rajr
I had a differential equation and I have also computed the general solution of the equation, but i want to check whether my simplification is right for the following

[−(e^−x)/(1 + e^x)] − [(e^−2x)/(1 + e^x)] = −e^(−2x)

Is this right...
$-\frac{e^{-x}}{1 + e^x} - \frac{e^{-2x}}{1 + e^x}$

$-\frac{e^{-x} + e^{-2x}}{1 + e^x}$

$-\frac{e^{-x}(1 + e^{-x})}{1 + e^x}$