+206 Simplify and rationalize the denominator:
$$\frac{1}{1+ \frac{1}{\sqrt{3}+1}}.$$
+129899 Npte that 1 + 1 / (sqrt 3 + 1) = (sqrt 3 + 1 + 1) / (sqrt 3 + 1) =
(sqrt (3) + 2 ) / (sqrt (3) + 1)
So the fraction simplifies to
sqrt (3) + 1
_________ multiply top/bottom by sqrt (3) - 2
sqrt (3) + 2
(sqrt (3) + 1) (sqrt (3) - 2)
_______________________
(sqrt (3) + 2) (sqrt (3) - 2)
3 - sqrt (3) - 2
____________
3 - 4
1 - sqrt (3)
________
-1
sqrt (3) - 1
