anonymous
  • anonymous
Simplify the following
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1347334599772:dw|
anonymous
  • anonymous
There isn't much you can do with that. You can try factoring. There's a difference of cubes up top, and the bottom is a square of sorts.
anonymous
  • anonymous
@CliffSedge I know that the answer should be 2013. I have no idea how to get there though

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anonymous
  • anonymous
Just to make sure we're looking at the same thing, is this what you wrote? \[\frac{8-27^n}{4+2 \cdot 3^n +9} \space +2011+3^n\]
anonymous
  • anonymous
yup
anonymous
  • anonymous
Well if the answer is 2013, then \[\frac{8-27^n}{4+2 \cdot 3^n +9} +3^n = 2.\]
anonymous
  • anonymous
Is it possible to add 2^2 to 2?
anonymous
  • anonymous
The top can be factored as a difference of cubes: \[8-27^n = 2^3-3^{3n} = (2-3^n)(4+2 \cdot 3^n+3^{2n})\]
anonymous
  • anonymous
What do you mean, "add 2^2 to 2?" 2^2 = 4, 4+2=6.
anonymous
  • anonymous
Are you sure that denominator isn't 4+2*3^n+9^n ?
anonymous
  • anonymous
Then it would work out just fine.
anonymous
  • anonymous
@CliffSedge Im sure, its just 9.
anonymous
  • anonymous
\[\frac{8-27^n}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow\] \[\frac{2^3-3^{3n}}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow\] \[\frac{(2-3^n)((4+2 \cdot 3^n +9^n)}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow\] \[2-3^n +2011+3^n =2013.\]
anonymous
  • anonymous
Well, that's unfortunate.

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