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Math Help - Asymptotes of a function

  1. #1
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    Asymptotes of a function

    Hello everyone

    I am asked to find the asymptotes of f(x)=\frac{x^2+1}{x+2}

    One of these is x=-2 , but when I try to arrive at the other asymptote, I get differing answers depending on the method I use.

    First I tried to simplify the function

    <br />
\frac{x^2 (1-\frac{1}{x^2})}{x(1+\frac{2}{x})}
    Looking at this it seems that when x approaches infinity, the function f(x) approaches the asymptote y=x.

    However, if I use long division of polynomials of nested synthetic division I always get that the function will approach y=x-2.
    Can someone please help me figure out what I'm doing wrong?
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  2. #2
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    (x^2 + 1) : (x + 2) = x -2 + \frac{5}{x + 2}
    -(x^2 + 2x)
    -------------
    -2x+1
    -(-2x - 4)
    -------------
    5

    yeah it is y = x -2

    I can't think of a way to do this with limits, since both x and y go to +- infinity.
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  3. #3
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    So why did the simplification yield a different result?
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