Answer
$\frac{\sqrt 5-1}{4}$
Work Step by Step
$\frac{1}{\sqrt 5+1}=\frac{1}{\sqrt 5+1}\frac{\sqrt 5-1}{\sqrt 5-1}=\frac{1(\sqrt 5-1)}{\sqrt 5(\sqrt 5)+\sqrt 5(-1)+1(\sqrt 5)-1(1)}=\frac{\sqrt 5-1}{(\sqrt 5)^2-1}=\frac{\sqrt 5-1}{5-1}=\frac{\sqrt 5-1}{4}$
