the domain for a rational expression will be the values of "x" that can safely be taken without setting the denominator to 0, since if that occurs the rational becomes undefined, well we can simply set the denominator to 0 and check which values are those.
[tex]\cfrac{x^2-x-20}{5x^2+18x-8}\implies \cfrac{(x-4)(x-5)}{(x+4)(5x-2)} \\\\\\ \stackrel{\textit{setting the denominator to 0}}{(x+4)(5x-2)=0}\implies x= \begin{cases} -4\\ \frac{2}{5} \end{cases}~\hfill \stackrel{\mathbb{DOMAIN}}{\{x|x\in \mathbb{R};x\ne -4,\frac{2}{5}\}}[/tex]
