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Math Help - differential equation (checking a simplification)

  1. #1
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    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...
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  2. #2
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    Quote Originally Posted by rajr View Post
    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}
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