Math Equation - Need help symplifying

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A user sought help simplifying a complex math equation, struggling with the steps involved. Another participant provided a detailed breakdown of the equation, clarifying how to handle fractions and common denominators. The explanation included step-by-step calculations, leading to a final simplified form of the equation. The original poster expressed gratitude for the assistance and acknowledged the clarity gained from the explanation. The discussion emphasized the importance of practicing similar problems to master the technique.
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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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The image isn't loading for me - could you possibly just type the equation in or is it too complex?


Oscar
 


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.
 
So is it like this?

<br /> 1+\cfrac{1}{x+\cfrac{1}{x+\cfrac{1}{x+\cfrac{1}{x+1}}}}<br />
 
Start with the bottom:
x+\frac{1}{x+1}=\frac{x^{2}+x+1}{x+1}

Now, the next calculation will be:

x+\frac{x+1}{x^{2}+x+1}=\frac{x^{3}+x^{2}+2x+1}{x^{2}+x+1}

You then have:

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}

Thus, we finally get:

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}
 
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Thanks, but could you explain your reasoning for doing each step?
 
Not unless you point specifically at what you didn't understand.
 
How did you get from step 2 to step 3? Such as how did 2x come into play?
 
How do you add fractions?
 
  • #10
Krasz said:
How did you get from step 2 to step 3? Such as how did 2x come into play?

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

Agreed thus far?

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

Calculate the numerator of this expression!
 
  • #11
arildno said:
After step 1, we have the following "bottom part":
x+\frac{1}{\frac{x^{2}+x+1}{x+1}}=x+\frac{x+1}{x^{2}+x+1}

Agreed thus far?

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

Calculate the numerator of this expression!

Thank you so much I see it now! You were a great help!
 
  • #12
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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