Question

how do I simplify the rational expression,2x-8÷2x^2+2x-40?

Answer 1

$\begin{gathered} \frac{2x-8}{2x^2+2x-40}=\frac{2(x-4)}{2(x^2+x-20)}=\frac{(x-4)}{x^2+x-20} \\ \text{Also} \\ x^2+x-20=(x+5)(x-4),\text{ then} \\ \frac{(x-4)}{x^2+x-20}=\frac{(x-4)}{(x+5)(x-4)}=\frac{1}{x+5} \\ \frac{2x-8}{2x^2+2x-40}=\frac{1}{x+5} \end{gathered}$