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Math Equation - Need help symplifying

  1. Sep 24, 2009 #1
    Hey guys i have been attempting this problem for days. If you can help me with it and explain how to solve it, I would be extremely grateful. I wrote my answer on the right. Thanks!!!
     

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  2. jcsd
  3. Sep 24, 2009 #2
    The image isn't loading for me - could you possibly just type the equation in or is it too complex?


    Oscar
     
  4. Sep 24, 2009 #3
    Re: Math Equation - Need help simplifying

    Ill give it a whirl.

    1+1/x+1/x+1/x+1/x+1

    Now, the second number in the equations is always the one being divided by x + 1.
    It is not both numbers that are divided, just the second. This series goes all the way down.
     
  5. Sep 24, 2009 #4

    statdad

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    So is it like this?

    [tex]
    1+\cfrac{1}{x+\cfrac{1}{x+\cfrac{1}{x+\cfrac{1}{x+1}}}}
    [/tex]
     
  6. Sep 25, 2009 #5

    arildno

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    Start with the bottom:
    [tex]x+\frac{1}{x+1}=\frac{x^{2}+x+1}{x+1}[/tex]

    Now, the next calculation will be:

    [tex]x+\frac{x+1}{x^{2}+x+1}=\frac{x^{3}+x^{2}+2x+1}{x^{2}+x+1}[/tex]

    You then have:

    [tex]x+\frac{x^{2}+x+1}{x^{3}+x^{2}+2x+1}=\frac{x^{4}+x^{3}+3x^{2}+2x+1}{x^{3}+x^{2}+2x+1}[/tex]

    Thus, we finally get:

    [tex]1+\frac{x^{3}+x^{2}+2x+1}{x^{4}+x^{3}+3x^{2}+2x+1}=\frac{x^{4}+2x^{3}+4x^{2}+4x+2}{x^{4}+x^{3}+3x^{2}+2x+1}[/tex]
     
    Last edited: Sep 25, 2009
  7. Sep 25, 2009 #6
    Thanks, but could you explain your reasoning for doing each step?
     
  8. Sep 25, 2009 #7

    arildno

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    Not unless you point specifically at what you didn't understand.
     
  9. Sep 25, 2009 #8
    How did you get from step 2 to step 3? Such as how did 2x come into play?
     
  10. Sep 25, 2009 #9

    Borek

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    How do you add fractions?
     
  11. Sep 25, 2009 #10

    arildno

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    After step 1, we have the following "bottom part":
    [tex]x+\frac{1}{\frac{x^{2}+x+1}{x+1}}=x+\frac{x+1}{x^{2}+x+1}[/tex]

    Agreed thus far?

    Now, we find a common denominator to the above sum:
    [tex]x+\frac{x+1}{x^{2}+x+1}=\frac{x*(x^{2}+x+1)+x+1}{x^{2}+x+1}[/tex]

    Calculate the numerator of this expression!
     
  12. Sep 25, 2009 #11
    Thank you so much I see it now! You were a great help!
     
  13. Sep 25, 2009 #12

    arildno

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    Even though they have not been assigned as exercises, I am sure your textbook contains a few more problems of the same type.

    Do some of them to make sure you master the technique on your own!

    Good luck! :smile:
     
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