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Math Help - Finding the standard form of a rational function

  1. #1
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    Finding the standard form of a rational function

    Find the standard form for (20x^2+11x-1)/(4x+3)?


    Not sure what 'standard' form means, help would be appreciated
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  2. #2
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    I'm not sure what is meant either, but maybe the requirement is to perform polynomial long division here?

    I.e make \displaystyle \frac{20x^2+11x-1}{4x+3} = a+\frac{b}{4x+3}
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    well after finding the standard form, I'm asked to find all straight line asymptotes (vertical, horizontal or oblique), maybe that might give a clue?
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  4. #4
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    Well now knowing this, my advice in post #2 is the way forward.
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    How do I find a and b? Would you be able to show me an example (I've got quite a few of these to do and seeing the steps would help a lot!)
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  6. #6
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    Polynomial long division is the road I would take.

    Follow this example

    Polynomial Long Division

    Spoiler:
    \displaystyle \frac{20x^2+11x-1}{4x+3} = 5x-1+\frac{2}{4x+3}
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    Thanks a lot, I really appreciate it
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  8. #8
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    Are you aware of what this means in context of the following question about asymptotes?
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  9. #9
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    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
    Last edited by brumby_3; March 30th 2011 at 06:18 PM.
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  10. #10
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    Quote Originally Posted by brumby_3 View Post
    Don't I have to find where (4x+3) is 0
    Yep, solve 4x+3=0, that is the vertical asymptote.



    Quote Originally Posted by brumby_3 View Post

    Is the slant/oblique asymptote just 5x-1?
    Yep!
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