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Math Help - Combining Algebra Fractions Frustration...

  1. #1
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    Combining Algebra Fractions Frustration...

    I've been working through an Algebra book trying to re-teach myself...not doing a half-bad job. I've come to a problem I'm not sure I understand. I reach the right answer...but yet it's wrong. I've attached the problem, along with the way I've been working it into a MS Word doc file. Any insight as to where I'm going wrong, ruels I'm forgetting or clarification on how the book comes to the answer it does would be greatly appreciated!

    A big thanks in advance!

    Ev
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  2. #2
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    You forgot one rule, not of mathematics but of internet security: Do not download files from an unknown source.

    You can use LaTeX to represent equations: http://www.mathhelpforum.com/math-he...-tutorial.html
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  3. #3
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    Oooops....
    I'll read through how to use the LaTeX tutorial and re-submit.
    Sorry and thanks!

    Ev
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  4. #4
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    My friend, you got the solution correct. The book is simply writing it in another way.

    Their answer has the negative sign in front of the entire fraction. To distribute it, you make every TERM in the numerator the opposite of what it is. In this case

    -(2x + 11) = -2x - 11

    Think about it this way

    2x + 11 is the same as +2x + 11, right?

    The negative of that -2x - 11.

    A helpful way to think about this is to set up a "thought experiment" with two simple numbers. For example:

    (5 - 3) = 2

    So the negative of that should equal negative 2, correct? Let's write:

    -(5 - 3) = -5 + 3 = -2

    Let me know if you have more questions. Sorry I typed this up very fast.
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  5. #5
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    Thank you so much for the reply.
    My only question is realy a clarification point...

    If I have a -x-23
    ------
    y-z
    (just for argument sake)

    I can make both terms in the numerator positive by making the entire fraction negative?:

    -x-23 = x+23
    ------- - -------
    y - z y - z

    If this is correct, I have a new confusion. If I remember right, you can change two signs of the fraction and still keep it equivalent to the original fraction. If I change the two signs in the numerator to positive and then change the sign of the fraction itself...then thats three signs changed, not two. Is it still equivalent?
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  6. #6
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    Quote Originally Posted by ejanderson View Post
    Thank you so much for the reply.
    My only question is realy a clarification point...

    If I have a -x-23
    ------
    y-z
    (just for argument sake)

    I can make both terms in the numerator positive by making the entire fraction negative?:

    -x-23 = x+23
    ------- - -------
    y - z y - z

    If this is correct, I have a new confusion. If I remember right, you can change two signs of the fraction and still keep it equivalent to the original fraction. If I change the two signs in the numerator to positive and then change the sign of the fraction itself...then thats three signs changed, not two. Is it still equivalent?
    That is fine. The original equation is

    \frac{-x-23}{y-z}

    given that any fraction with equal numerator and denominator is 1 then we can multiply by \frac{-1}{-1}

    \frac{-x-23}{y-z} \times \frac{-1}{-1} = \frac{-1(-x-23)}{-1(y-z)} = \frac{x+23}{-(y-z)} = -\frac{x+23}{y-z}

    Which is the answer you got.

    We can also distribute that minus sign on the denominator instead of leaving it (in the penultimate step):

    \frac{x+23}{z-y}


    You mention changing 3 signs but you have to in order to ensure the equation is still the same. When you're changing the sign you're actually distributing -1 across the term inside the brackets
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