$\displaystyle \frac{\sqrt{5}-1}{\sqrt{5}+3}$ Rewrite the expression with a rational denominator

I start by multiplying top and bottom by $\displaystyle \sqrt{5}-3$

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

Is my next step correct please?

$\displaystyle =\frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}$