Question

(1-4/x)/(1-2/x-8/x^2 )

Answer 1

A substitution might make it more convenient. Let u = 1/x. Then we can say\[\frac{1-\frac{4}{x}}{1-\frac{2}{x}-\frac{8}{x^2} }=\frac{4u-1}{8u^2+2u-1}=\frac{4u-1}{(4u-1)(2u+1)}=\frac{1}{\frac{2}{x}+1}\]Your teacher or the author of your text might want a little more simplification, but this should get you started.