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Thread: A simple algebra equation

  1. #1
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    Question A simple algebra equation

    How can we express x if we have

    $$ x = (y - x) e^z$$
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  2. #2
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    Re: A simple algebra equation

    Quote Originally Posted by brianx View Post
    How can we express x if we have

    $$ x = (y - x) e^z$$
    $x=\dfrac{ye^z}{1+e^z}$
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  3. #3
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    Re: A simple algebra equation

    From x= (y- x)e^z, first do the indicated multiplication- x= ye^z- xe^z.

    Now add xe^z to both sides- x+ xe^z= ye^z.

    Factor out x- x(1+ e^z)= ye^z.

    Finally, divide both sides by 1+ e^z-

    x= \frac{ye^z}{1+ e^z}.
    Thanks from brianx
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  4. #4
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    Re: A simple algebra equation

    With one caveat:

    $x = \begin{cases}x \in \mathbb{C} & z = \pi i(2n+1), n\in \mathbb{Z} \\ \dfrac{ye^z}{1+e^z} & \text{otherwise}\end{cases}$

    In other words, if $e^z = -1$, then $y=0$ and $x$ can be any complex number. Otherwise, it equals the fraction Plato and HallsofIvy gave.
    Last edited by SlipEternal; Aug 23rd 2017 at 06:01 AM.
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