\( rac{-\sqrt{5}+1}{-\sqrt{5}-1} = rac{\sqrt{5}-1}{\sqrt{5}+1} = rac{(\sqrt{5}-1)^2}{5 - 1} = rac{6 - 2\sqrt{5}}{4} \), but we earlier derived it correctly as \( rac{3 - \sqrt{5}}{2} \), so it checks.