# Thread: A simple algebra equation

1. ## A simple algebra equation

How can we express x if we have

$$x = (y - x) e^z$$

2. ## Re: A simple algebra equation

Originally Posted by brianx
How can we express x if we have

$$x = (y - x) e^z$$
$x=\dfrac{ye^z}{1+e^z}$

3. ## 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 $1+ e^z$-

$x= \frac{ye^z}{1+ e^z}$.

4. ## 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.