# Thread: Factoring a complex equation

1. ## Factoring a complex equation

Hi,

Can someone help me figure out how to factor $\frac{e}{x^2} - e^3$ so that I get some factor, y, such that y(x - $\frac{1}{e}$) = $\frac{e}{x^2} - e^3$?

I'm having quite a tough time figuring out what y should be

2. ## Re: Factoring a complex equation

well it's pretty clear that

$y = \dfrac{\frac{e}{x^2}-e^3}{x-\frac 1 e},~\forall x \neq \dfrac 1 e$

$y = \dfrac{\frac{e-x^2e^3}{x^2}}{\frac{xe-1}{e}}$

$y = \dfrac{e^2(1-x^2 e^2)}{x^2(xe-1)}$

This can be simplified a bit further

$y = -\dfrac{e^2(1-xe)(1+xe)}{x^2(1-xe)} = -\dfrac{e^2(1+x e)}{x^2}$