$$((1/2)*(1/2))/((1/\sqrt2)-1)\\\\
=\frac{1}{4}\div \frac{1-\sqrt2}{\sqrt2}\\\\
=\frac{1}{4}\times \frac{\sqrt2}{1-\sqrt2}\\\\
=\frac{1}{4}\times \frac{\sqrt2}{1-\sqrt2}\times \frac{1+\sqrt2}{1+\sqrt2}\\\\
=\frac{1}{4}\times \frac{\sqrt2(1+\sqrt2)}{1-2}\\\\
=\frac{\sqrt2(1+\sqrt2)}{-4}\\\\
=\frac{-2-\sqrt2)}{4}\\\\$$
$$((1/2)*(1/2))/((1/\sqrt2)-1)\\\\
=\frac{1}{4}\div \frac{1-\sqrt2}{\sqrt2}\\\\
=\frac{1}{4}\times \frac{\sqrt2}{1-\sqrt2}\\\\
=\frac{1}{4}\times \frac{\sqrt2}{1-\sqrt2}\times \frac{1+\sqrt2}{1+\sqrt2}\\\\
=\frac{1}{4}\times \frac{\sqrt2(1+\sqrt2)}{1-2}\\\\
=\frac{\sqrt2(1+\sqrt2)}{-4}\\\\
=\frac{-2-\sqrt2)}{4}\\\\$$