`...=(sqrt3(sqrt2-1))/(sqrt2-1)+(2(sqrt2-1))/((sqrt2+1)(sqrt2-1))-(sqrt3(sqrt3+1))/(sqrt3+1)-(4sqrt2)/2=sqrt3+2sqrt2-2-sqrt3-2sqrt2=-2`
\(\dfrac{\sqrt{6}-\sqrt{3}}{\sqrt{2}-1}+\dfrac{2}{\sqrt{2}+1}-\dfrac{3+\sqrt{3}}{\sqrt{3}+1}-\dfrac{4}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}+\dfrac{2}{\sqrt{2}+1}-\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}-\dfrac{2.\sqrt{2^2}}{\sqrt{2}}\)
\(=\sqrt{3}+\dfrac{2}{\sqrt{2}+1}-\sqrt{3}-2\sqrt{2}\)
\(=\left(\sqrt{3}-\sqrt{3}\right)+\left(\dfrac{2}{\sqrt{2}+1}-2\sqrt{2}\right)\)
\(=\dfrac{2-2\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}\)
\(=\dfrac{2-4-2\sqrt{2}}{\sqrt{2}+1}\)
\(=\dfrac{-2-2\sqrt{2}}{\sqrt{2}+1}\)
\(=\dfrac{-2\left(1+\sqrt{2}\right)}{\sqrt{2}+1}\\ =-2\)
