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Math Help - Finding the Oblique asymptote

  1. #1
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    Finding the Oblique asymptote

    I have this equation,

    3x^2-16x-12 / x+5

    I have to find all of the Asymptotes, Since the numerator is larger then the denominator I know that I need to use long division. I also assume since the Denominator is larger I have a OA instead of an HA. When I graph this function it looks similar to a typical transformed X^2 function. After doing the long division I got OA of 3x-31. Does this need to be simplified more? Also, am I thinking of this problem correctly?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Finding the Oblique asymptote

    You have found the correct OA, and no further simplification is necessary, as you have it in slope-intercept form.

    Rather than perform division, you may also get the same result by writing:

    y=\frac{3x^2-16x-12}{x+5}=\frac{3(x+5)^2-46(x+5)+143}{x+5}=

    3(x+5)-46+\frac{143}{x+5}=3x-31+\frac{143}{x+5}

    Although, it is perhaps more straightforward to perform the division.
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