+0

+1
31
4
+63

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.

May 2, 2021

#1
+758
+2

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

May 2, 2021
#2
+63
+1

May I ask how you got that?

grs75  May 2, 2021
#3
+758
+3

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
#4
+63
+1

Oh okay, thanks!

grs75  May 2, 2021