How do you solve  4/(x^2-2x-3) = [-x/(x-3)] [-1/(x+1)]?

Oct 23, 2015

$x = 4$

Explanation:

Start by simplifying the right side:
color(white)("XXX")(-x/(x-3))(-1/(x+1))=x/(x^2-2x-3

So the given equation is equivalent to
$\textcolor{w h i t e}{\text{XXX}} \frac{4}{{x}^{2} - 2 x - 3} = \frac{x}{{x}^{2} - 2 x - 3}$

$\Rightarrow \textcolor{w h i t e}{\text{XXX}} x = 4$

This, of course, assumes $x \ne 3$ and $x \ne - 1$; otherwise the original equation is meaningless.