I'm not sure what is meant either, but maybe the requirement is to perform polynomial long division here?
I just did all the working out for the question using the example, thanks a lot! For the asymptotes, I'm not sure how to figure them out in this form. Don't I have to find where (4x+3) is 0 so that it is infinity or something along those lines?
Is the slant/oblique asymptote just 5x-1? and I think there is no vertical or horizontal asymptotes