Hello guys,

Could somebody help me simplify this fraction:

\(\dfrac{\tfrac{x-\sqrt{3}}{x\sqrt{3}+1}-\sqrt{3}}{\tfrac{x-\sqrt{3}}{x\sqrt{3}+1}\sqrt{3}+1}\)

I've tried rationalizing it several times, but I keep getting lost.

Thanks in advance!

grs75 May 2, 2021

#1**+2 **

A simpler form of this fraction is $\dfrac{x + \sqrt{3}}{1 - x\sqrt{3}}$. Can you take it from here?

CentsLord May 2, 2021

#3**+4 **

Just multiplied the entire fraction by $\dfrac{x\sqrt{3} + 1}{x\sqrt{3} + 1}.$

Compose the function a few more times, and you'll likely be able to find a pattern which'll enable you to find $f^{2012}(x)$. I know the broader problem this is part of, did it several weeks ago. good luck

CentsLord
May 2, 2021