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Math Help - Simple algebraic sum

  1. #1
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    Simple algebraic sum

    I have this algebraic fraction sum I need help with.
    Code:
    x^2 - 7x
    -------
    x^2 - 49
    I worked it out by cancelling out the x^2 on both sides, and then simplifing the rest, and my answer was:

    Code:
    x
    --
    7
    I read that the correct method would be this:
    Code:
       x(x-7)            x
    ---------      =   ----
    (x+7)(x-7)          x-7
    Why is this right, and my method wrong? My reasoning is that the denominators are the same for x^2 and 7x, so I can just work by simplifying them...
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  2. #2
    Newbie liptak's Avatar
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    Hey,

    there is a formula a^2 - b^2 = (a+b)*(a-b). You have to use this formula on your denominator.

    Liptak
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  3. #3
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    Yep thats factorising for difference of squares. I want to know why use that when I can just simplify the sum the way I did.
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  4. #4
    Newbie liptak's Avatar
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    You can't cancel out the x^2 on both sides, beacause there is a minus sign between the elements. You could do it if there was a multiplication only...
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  5. #5
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    \frac{7- 5}{7- 2}= \frac{2}{5} NOT \frac{-5}{-2}= \frac{5}{2}. You can cancel like terms when they are multiplied by the rest of the numerator or denominator, not when they are added to them.
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  6. #6
    MHF Contributor
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    Quote Originally Posted by yorkey View Post
    Code:
       x(x-7)            x
    ---------      =   ----
    (x+7)(x-7)          x-7
    Should be x / (x + 7).

    Let (as example) x = 8 and see what happens your way...
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