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Math Help - Rewriting an expression without the absolute value symbols

  1. #1
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    Rewriting an expression without the absolute value symbols

    \frac{|x-y|}{|y-x|}<br />
    x cannot equal y.
    I'm stumped on this, I'm being told the answer is 1 but I don't understand how.
    If someone could explain this indepth I'd be so grateful! Thank you.
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  2. #2
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    Quote Originally Posted by tiar View Post
    \frac{|x-y|}{|y-x|}<br />
    x cannot equal y.
    I'm stumped on this, I'm being told the answer is 1 but I don't understand how.
    If someone could explain this indepth I'd be so grateful! Thank you.
    Let x-y=z

    Then \frac{|x-y|}{|y-x|} = \frac{|z|}{|-z|} = \frac{|z|}{|z|} = 1
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  3. #3
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    Ohh, I think I get it now. Thank you! I'm very bad with absolute value...
    Edit: Wait, I'm still confused. Where does \frac{|x-y|}{|-x-y|} Come from?
    (That is, \frac{|z|}{|-z|})
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  4. #4
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    Quote Originally Posted by tiar View Post
    Ohh, I think I get it now. Thank you! I'm very bad with absolute value...
    Edit: Wait, I'm still confused. Where does \frac{|x-y|}{|-x-y|} Come from?
    (That is, \frac{|z|}{|-z|})
    If z = x - y then

    -z = (-1)(x - y) = -x + y = y - x
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  5. #5
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    Quote Originally Posted by tiar View Post
    Wait, I'm still confused. Where does \frac{|x-y|}{|-x-y|} Come from?
    If you do 5 - 3, you get +2.

    If you do 3 - 5, you get -2.

    If you reverse a subtraction, you kick a "minus" out front.

    Have fun!
    Last edited by mr fantastic; January 14th 2009 at 05:11 AM. Reason: Fixed quote tags
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