`a)`
`1/(\sqrt{3} + \sqrt{2}) - (\sqrt{6})/(\sqrt{3}) + 3 \sqrt{1/3}`
`= 1/(\sqrt{3} + \sqrt{2}) - \sqrt{2} + \sqrt{3}`
` = (1 - \sqrt{2} (\sqrt{3} + \sqrt{2}) + \sqrt{3} ( \sqrt{3} + \sqrt{2}))/(\sqrt{3} + \sqrt{2}) `
` = (1 - \sqrt{6} - \sqrt{4} + \sqrt{9} + \sqrt{6})/(\sqrt{3} + \sqrt{2}) `
` = (1 - \sqrt{4} + \sqrt{9})/(\sqrt{3} + \sqrt{2})`
` = (1- 2 + 3)/(\sqrt{3} + \sqrt{2}) `
` = 2/(\sqrt{3} + \sqrt{2}) `
`= 2 \sqrt{3} - 2 \sqrt{2}`
`b)`
`\sqrt{5 - 2 \sqrt6} (\sqrt{3} + \sqrt{2})`
` = \sqrt{ 3 - 2 \sqrt6} + 2 } (\sqrt{3} + \sqrt{2})`
`= \sqrt{ (\sqrt{3})^2 - 2 . \sqrt{3} . \sqrt{2} + (\sqrt{2})^2 } (\sqrt{3} + \sqrt{2})`
`= \sqrt{ (\sqrt{3} - \sqrt{2})^2 } (\sqrt{3} + \sqrt{2})`
`= |\sqrt{3} - \sqrt{2}| (\sqrt{3} + \sqrt{2})`
`= (\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2})`
`= (\sqrt{3})^2 - (\sqrt{2})^2`
` = 3-2`
`= 1`