## Mello 3 years ago Simplify the following

1. Mello

|dw:1347334599772:dw|

2. CliffSedge

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.

3. Mello

@CliffSedge I know that the answer should be 2013. I have no idea how to get there though

4. CliffSedge

Just to make sure we're looking at the same thing, is this what you wrote? $\frac{8-27^n}{4+2 \cdot 3^n +9} \space +2011+3^n$

5. Mello

yup

6. CliffSedge

Well if the answer is 2013, then $\frac{8-27^n}{4+2 \cdot 3^n +9} +3^n = 2.$

7. Mello

Is it possible to add 2^2 to 2?

8. CliffSedge

The top can be factored as a difference of cubes: $8-27^n = 2^3-3^{3n} = (2-3^n)(4+2 \cdot 3^n+3^{2n})$

9. CliffSedge

What do you mean, "add 2^2 to 2?" 2^2 = 4, 4+2=6.

10. CliffSedge

Are you sure that denominator isn't 4+2*3^n+9^n ?

11. CliffSedge

Then it would work out just fine.

12. Mello

@CliffSedge Im sure, its just 9.

13. CliffSedge

$\frac{8-27^n}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow$ $\frac{2^3-3^{3n}}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow$ $\frac{(2-3^n)((4+2 \cdot 3^n +9^n)}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow$ $2-3^n +2011+3^n =2013.$

14. CliffSedge

Well, that's unfortunate.