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Thread: Combine these into a single equivalent fraction;

  1. #1
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    Combine these into a single equivalent fraction;

    Combine these into a single equivalent fraction;

    3/K - 4 + K + 4/K^2 - 16

    I factored k^2 - 16 so that its (k - 4) (k + 4)

    The k + 4 cancel out as like expressions

    and I end up with k - 4 as the denominator and 3 as the numerator such as..

    3/k - 4

    Is this correct?

  2. #2
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    Here is what you have written:

    [tex]\frac{3}{K} - 4 + k + \frac{4}{k^{2}} - 16[/tex]

    I assume you mean [tex]\frac{3}{k-4}+\frac{k+4}{k^{2}-16}[/tex]

    I am only guessing. Without proper grouping symbols, it can mean various things.

  3. #3
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    Quote Originally Posted by galactus View Post
    Here is what you have written:

    [tex]\frac{3}{K} - 4 + k + \frac{4}{k^{2}} - 16[/tex]

    I assume you mean [tex]\frac{3}{k-4}+\frac{k+4}{k^{2}-16}[/tex]

    I am only guessing. Without proper grouping symbols, it can mean various things.
    Yes, that is the correct Interpretation .

  4. #4
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    Quote Originally Posted by JeffM View Post
    Now that we know that, we can explain why your answer is wrong. It greatly helps to show your work. You will catch many of your own errors if you do.

    [TEX]\dfrac{3}{k-4}+\dfrac{k+4}{k^2-16} = [/TEX]

    [TEX]\dfrac{3}{k-4}+\dfrac{k+4}{(k + 4)(k-4)} =[/TEX]

    [TEX]\dfrac{3}{k-4} + \dfrac{1}{k-4} =[/TEX]

    [TEX]\dfrac{4}{k-4}.[/TEX]

    How did you get 1 from (k + 4) and then add it to 3 to get 4 for the numerator?

    Oh, I see you eliminated (k + 4) in both numerator and denominators and your left with a 1 for the numerator?
    Last edited by gijas; 11-19-2011 at 02:34 PM.

  5. #5
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    one restriction should be included:

    [TEX]k \ne \pm 4[/TEX]
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  6. #6
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    Quote Originally Posted by gijas View Post
    3/K - 4 + K + 4/K^2 - 16
    Next time make SURE you bracket properly: 3 / (K - 4) + (K + 4) / (K^2 - 16)
    I'm just an imagination of your figment !

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