While I was studying my maths book, I came across this equation:
$ xe^{-x}+2e^{-x}=0 $
I tried to solve it in different ways, but each time I break up some rule. My best try was this:
Let's $u=e^{-x}$, thus we have: $ xu+2u=0 $ By taking $u$ as a common factor we get:
$ u(x+2)=0 $
By dividing both side by $(x+2)$ we get:
$ u=0 $
But $u=e^{-x}$, then:
$ e^{-x}=0 \\ ln(e^{-x}) = ln(0) ?? $
$ln(0)$ is obviously wrong, where did I slip?