Finding oblique asymptotes help

hi im new here =], and i was just wondering how do yo find oblique asymptotes for functions f(x) = P(x)/Q(x). i know to find horizontal asymptotes you take the limit x--> infinity, but how do you find the asymptote if the degree of the numerator is higher than the denominator. By the way, no long division, as we have not done it in class yet.

An example question would be y = x/4 + 1/x where the oblique asymptote is y=x/4


EDIT: oops sorry i meant the answer to the question is y=x/4 (the oblique asymptote) and we havent done long division, its not in our 2 unit course (if you know what that means) and its in next year's course.

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Originally Posted by noobonastick

hi im new here =], and i was just wondering how do yo find oblique asymptotes for functions f(x) = P(x)/Q(x). i know to find horizontal asymptotes you take the limit x--> infinity, but how do you find the asymptote if the degree of the numerator is higher than the denominator. By the way, no long division, as we have not done it in class yet.

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finding oblique asymptotes are usually done using long division or synthetic division. otherwise, the problem has to be really nice where you "see" it

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An example question would be y = x/4 + 1/x where the oblique asymptote is y=x/4

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...i am confused. how is this a problem on finding the oblique asymptote? it's given

if you were given y = x/4 + 1/x to find the oblique asymptote, you could use long division. or you just take the polynomial part, which in this case is x/4

we know we can take the polynomial part because, had we done long division, the quotient would be a polynomial and the remainder would not