Question

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

Answer 1

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