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Math Help - Another Limits Question

  1. #1
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    Another Limits Question

    I have the following question on a worksheet:

    <br />
lim ((2/x+2)-(3/x-1))/(x+8)<br />

    With x approaching 8.

    I simplified the equation to:

    <br />
 lim ((2x-2)-(3x+6))/((x-1)(x+2))/(x+8)<br />

    I Know that I should factor out the denominator in the upper portion, but I am unsure as to how I would do so.
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  2. #2
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    Quote Originally Posted by Jd09 View Post
    I have the following question on a worksheet:

    <br />
lim ((2/x+2)-(3/x-1))/(x+8)<br />

    With x approaching 8.

    I simplified the equation to:

    <br />
lim ((2x-2)-(3x+6))/((x-1)(x+2))/(x+8)<br />

    I Know that I should factor out the denominator in the upper portion, but I am unsure as to how I would do so.
    \displaystyle \frac{\frac{2}{x+2} - \frac{3}{x-1}}{x+8} = \frac{2(x-1)-3(x+2)}{(x+8)(x+2)(x-1)} = \frac{-x -8}{(x+8)(x+2)(x-1)}
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  3. #3
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    Actually for this one you don't need to simplify it first. You can plug x = 8 in directly. Always try this first and see if there is a Mathematical problem in doing so. Then you know if you have to try to simplify it.

    -Dan
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  4. #4
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    Quote Originally Posted by topsquark View Post
    Actually for this one you don't need to simplify it first. You can plug x = 8 in directly. Always try this first and see if there is a Mathematical problem in doing so. Then you know if you have to try to simplify it.

    -Dan
    I suspect the OP has made a typo and it's x --> -8 rather than 8.
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