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Math Help - Removable or Non Removable?

  1. #1
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    Removable or Non Removable?

    "Find the x-values(if any) at which f is not continuous. Which of the discontinuites are removable?"

    the funtion is f(x)=x-3/x^2-9

    Ok so I know its discontinuous at 3. But is it removable or non removable? and why? Do you need to know the graph to determine this? Thanks.
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  2. #2
    Eater of Worlds
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    Notice the difference of two squares in the denominator?.

    \frac{x-3}{(x-3)(x+3)}

    Now, see it?. You got a hole at x=3
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  3. #3
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    would that be removable or non? and why? Thanks.
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  4. #4
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    It is removeable.
    f(x) = \left\{ {\begin{array}{lr}<br />
   {\frac{{x - 3}}{{x^2  - 9}}} & {x \ne 3}  \\<br />
   {\frac{1}{6}} & {x = 3}  \\<br />
\end{array}} \right.<br /> <br />
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