e: \(\dfrac{3\sqrt{5}-2\sqrt{2}}{2\sqrt{5}-3\sqrt{2}}=\dfrac{18+5\sqrt{10}}{2}\)

`= ((1-sqrta)(1-sqrta))/((sqrta+1)(sqrta-1))`

`=-(1-2 sqrt a +a)/(a-1)``

\(\dfrac{1-\sqrt{a}}{1+\sqrt{a}}=\dfrac{\left(1-\sqrt{a}\right)\left(1-\sqrt{a}\right)}{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)}=\dfrac{1-2\sqrt{a}+a}{1-a}\)

\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}{2}\)

\(\dfrac{-2}{3\sqrt{11}}\\ =\dfrac{-2\sqrt{11}}{3\cdot11}\\ =\dfrac{-2\sqrt{11}}{33}\)

d) \(=\dfrac{5\sqrt{2}\left(\sqrt{5}-\sqrt{2}\right)}{5-2}\) \(=\dfrac{5\sqrt{10}-10}{3}\)

e) \(=\dfrac{-5\left(\sqrt{6}-1\right)}{6-1}\) \(=\dfrac{-5\left(\sqrt{6}-1\right)}{5}\) \(=1-\sqrt{6}\)

\(=\dfrac{3\sqrt{5}+3}{2}\)

\(=\dfrac{3+\sqrt{5}}{2}\)