`a)` `frac{5-\sqrt{5}}{1-\sqrt{5}}+frac{3}{\sqrt{2}+\sqrt{5}}-\sqrt{5-2\sqrt{6}}`
`=(\sqrt5(\sqrt5-1))/-(\sqrt{5}-1)+((\sqrt5-\sqrt2)(\sqrt5+\sqrt2))/(\sqrt5+\sqrt2)-\sqrt{(\sqrt{3}-\sqrt{2})^2}`
`=-\sqrt{5}+\sqrt{5}-\sqrt{2}-|\sqrt{3}-\sqrt{2}|`
`=-\sqrt{2}-(\sqrt{3}-\sqrt{2})` (do `\sqrt{3}-\sqrt{2}>0)`
`=-\sqrt{2}-\sqrt{3}+\sqrt{2}`
`=-\sqrt{3}`
`b)` `4/\sqrt2-1/(\sqrt2+1)-(3\sqrt2-2)/(3-\sqrt2)`
`=(2\sqrt2.\sqrt2)/\sqrt2-((\sqrt2-1)(\sqrt2+1))/(\sqrt2+1)-(\sqrt2(3-\sqrt2))/(3-\sqrt2)`
`=2\sqrt{2}-(\sqrt{2}-1)-\sqrt{2}`
`=2\sqrt{2}-\sqrt{2}+1-\sqrt{2}`
`=1`
