Question 964496
Dividing function f by function g must result in {{{(x-2)/(x^2+7x)}}}.


I use here g for g(x), the unknown function.


{{{f/g=(1/x)/g=(x-2)/(x^2+7x)}}}


{{{1/(x*g)=(x-2)/(x^2+7x)}}}


{{{xg=(x^2+7x)/(x-2)}}}


{{{highlight(g=(x^2+7x)/(x(x-2)))}}}, and do not simplify this any further, because doing so will change part of the meaning of the function g.  g(x) currently is shown to have vertical asymtptote for x=0, and for x=2.