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Math Help - Simplifying complicated fraction.

  1. #1
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    Simplifying complicated fraction.

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     1+ \frac {2}{1+\frac{2}{x+\frac{2}{x}}} and  \frac{3x^2+2x+6}{x^2+2x+2} are equal when x = 2 and x = -1.

    True or False?/ They are equivalent expressions on (-infinity,infinity)

    I'm lost. How do you do this?

    Thank you!
    Last edited by mr fantastic; February 1st 2010 at 01:35 AM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by Anemori View Post
    show
     1+ \frac {2}{1+\frac{2}{x+\frac{2}{x}2}} and  \frac{3x^2+2x+6}{x^2+2x+2} are equal when x = 2 and x = -1.

    True or False?/ They are equivalent expressions on (-infinity,infinity)

    I'm lost. How do you do this?

    Thank you!
    Start simplifying the left hand equation.
     1+ \frac {2}{1+\frac{2}{\frac{x^2}{x}+\frac{2}{x}}}
     1+ \frac {2}{1+\frac{2}{\frac{x^2+2}{x}}}
     1+ \frac {2}{1+\frac{2x}{x^2+2}}
    1+ \frac{2}{\frac{x^2+2}{x^2+2} + \frac{2x}{x^2+2}}
    1+ \frac{2}{\frac{x^2+2x+2}{x^2+2}}
    1+ \frac{2(x^2+2)}{x^2+2x+2}
    \frac{x^2+2x+2}{x^2+2x+2}+\frac{2x^2+4}{x^2+2x+2}
    \frac{3x^2+2x+6}{x^2+2x+2}




    Last edited by 1005; January 31st 2010 at 09:24 AM.
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  3. #3
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    edit: your post is gone now i look silly :P
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  4. #4
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    It looks false . on the fraction i will evaluate the bottom part first going up?
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  5. #5
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    Quote Originally Posted by Anemori View Post
    It looks false . on the fraction i will evaluate the bottom part first going up?
    No, it's true. The math I showed was for when you had that extra two multiplied in. I have corrected my work to reflect your correction in the problem given.
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  6. #6
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    Quote Originally Posted by 1005 View Post
    No, it's true. The math I showed was for when you had that extra two multiplied in. I have corrected my work to reflect your correction in the problem given.
    let me see it
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  7. #7
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    Quote Originally Posted by Anemori View Post
    let me see it
    Quote Originally Posted by 1005 View Post
    Start simplifying the left hand equation.
     1+ \frac {2}{1+\frac{2}{\frac{x^2}{x}+\frac{2}{x}}}
     1+ \frac {2}{1+\frac{2}{\frac{x^2+2}{x}}}
     1+ \frac {2}{1+\frac{2x}{x^2+2}}
    1+ \frac{2}{\frac{x^2+2}{x^2+2} + \frac{2x}{x^2+2}}
    1+ \frac{2}{\frac{x^2+2x+2}{x^2+2}}
    1+ \frac{2(x^2+2)}{x^2+2x+2}
    \frac{x^2+2x+2}{x^2+2x+2}+\frac{2x^2+4}{x^2+2x+2}
    \frac{3x^2+2x+6}{x^2+2x+2}




    After simplifying the equation of the left, you see that they are exactly the same equation.
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  8. #8
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    1+\frac {2}{1+\frac{2}{x+\frac{2}{x}}}

    how did you do it from that to this:



    1+\frac {2}{1+\frac{2}{\frac{x^2}{x}+\frac{2}{x}}}<br />
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  9. #9
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    Quote Originally Posted by Anemori View Post
    1+\frac {2}{1+\frac{2}{x+\frac{2}{x}}}

    how did you do it from that to this:



    1+\frac {2}{1+\frac{2}{\frac{x^2}{x}+\frac{2}{x}}}<br />
    I multiplied by \frac{x}{x} which simplifies to 1. You can do that, because 1 X anything = that same anything. I did this so the two fractions at the bottom would have the same denominator, allowing them to be added. If you continue to look at what I did, I used that method about five times to add the fractions to 1.
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