#### Answer

$\frac{-4}{3(1+\sqrt{5})}$

#### Work Step by Step

We simplify the fraction by multiplying through by $1+\sqrt{5}$ and using the fact that $(a-b)(a+b)=a^2-b^2$:
$\displaystyle \frac{1-\sqrt{5}}{3}=\frac{1-\sqrt{5}}{3}* \displaystyle \frac{1+\sqrt{5}}{1+\sqrt{5}}=\frac{1-5}{3(1+\sqrt{5})}=\frac{-4}{3(1+\sqrt{5})}$