$\displaystyle \begin{array}{{>{\displaystyle}l}} a,\ \frac{3-2\sqrt{2}}{1-\sqrt{2}} =\frac{\left( 1-\sqrt{2}\right)^{2}}{1-\sqrt{2}} =1-\sqrt{2}\\ b.\ \frac{m\sqrt{n} -n\sqrt{m}}{m-n} =\frac{\sqrt{mn}\left(\sqrt{m} -\sqrt{n}\right)}{\left(\sqrt{m} +\sqrt{n}\right)\left(\sqrt{m} -\sqrt{n}\right)} =\frac{\sqrt{mn}}{\sqrt{m} +\sqrt{n}}\\ c.\ \frac{a}{b-1}\sqrt{\frac{( b-1)^{4}}{a^{2}}} =\ \frac{a}{b-1}\frac{( b-1)^{2}}{a} =b-1\\ \end{array}$
