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Math Help - Finding Oblique Asymptote

  1. #1
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    Finding Oblique Asymptote

    Hi all,

    I'm currently having the hardest time understanding how to find the Oblique Asymptote.

    An example is x^2 -1 / x + 3. I know I have to use long division method to figure this out but I don't even know how to start on such a simple one as this. Can someone give me a detailed method of doing this? Thanks alot~
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  2. #2
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    If you long divide you get:

    \frac{x^{2}-1}{x+3}=\underbrace{\frac{8}{x+3}}_{\text{r(x)/h(x)}}+\underbrace{x-3}_{\text{ax+b}}

    \lim_{x\rightarrow{\infty}}\frac{r(x)}{h(x)}=0

    Therefore, f(x) approaches the line y=ax+b as x increases or decreases without bound.

    Hence, your asymptote is y=x-3
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  3. #3
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    Quote Originally Posted by galactus View Post
    If you long divide you get:

    \frac{x^{2}-1}{x+3}=\underbrace{\frac{8}{x+3}}_{\text{r(x)/h(x)}}+\underbrace{x-3}_{\text{ax+b}}

    \lim_{x\rightarrow{\infty}}\frac{r(x)}{h(x)}=0

    Therefore, f(x) approaches the line y=ax+b as x increases or decreases without bound.

    Hence, your asymptote is y=x-3

    Thanks but I was wondering how to do the division part step by step
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  4. #4
    Eater of Worlds
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    Oh. I would suggest getting an algebra book and practicing. You really should be able to do that at this level.

    But here goes this one:

    Code:
         
          x     -3
          ____________________
    x+3|x^2      -1
          x^2+3x
         ---------------------------
                -3x-1
                -3x-9
        -------------------------------
                      8
    So, you have: \frac{8}{x+3}+x-3

    It works just like other division.
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