`a) A = 4/(\sqrt{5} - 1) + 2/(1 - \sqrt{3}) - 2/(\sqrt{3} - \sqrt{5})`

`A = 4(\sqrt{5} + 1)/4 + 2(1 + \sqrt{3})/(-2) - 2(\sqrt{3} + \sqrt{5})/(-2)`

`A = (\sqrt{5} + 1) - (1 + \sqrt{3}) + (\sqrt{3} + \sqrt{5})`

`A = \sqrt{5} + 1 - 1 - \sqrt{3} + \sqrt{3} + \sqrt{5}`

`A = 2\sqrt{5}`

`b) B = \sqrt{2} + 1/\sqrt{5 + 2\sqrt{6}} + 2/\sqrt{8 + 2\sqrt{15}}`

`B = \sqrt{2} + 1/(\sqrt{3} + \sqrt{2}) + 2/(\sqrt{5} + \sqrt{3})`

`B = \sqrt{2} + (\sqrt{3} - \sqrt{2})/(3 - 2) + 2(\sqrt{5} - \sqrt{3})/(5 - 3)`

`B = \sqrt{2} + \sqrt{3} - \sqrt{2} + \sqrt{5} - \sqrt{3}`

`B = \sqrt{5}`

`c) C = [ 24/(\sqrt{7} + 1) + 4/(3 + \sqrt{7}) - 3/(\sqrt{7} + 2) ] (4 - \sqrt{7})`

`C = [ 24(\sqrt{7} - 1)/6 + 4(3 - \sqrt{7})/2 - 3(\sqrt{7} - 2)/3 ] (4 - \sqrt{7})`

`C = [ 4(\sqrt{7} - 1) + 2(3 - \sqrt{7}) - (\sqrt{7} - 2) ] (4 - \sqrt{7})`

`C = (4\sqrt{7} - 4 + 6 - 2\sqrt{7} - \sqrt{7} + 2) (4 - \sqrt{7})`

`C = (\sqrt{7} + 4)(4 - \sqrt{7})`

`C = (4 + \sqrt{7})(4 - \sqrt{7})`

`C = 16 - 7`

`C = 9`

`d) D = [ 15/(3 - \sqrt{3}) - 2/(1 - \sqrt{3}) + 3/(\sqrt{3} - 2) ] . \sqrt{28 + 10\sqrt{3}}`

`D = [ 15(3 + \sqrt{3})/6 - 2(1 + \sqrt{3})/(-2) + 3(\sqrt{3} + 2)/(-1) ] . \sqrt{(5 + \sqrt{3})^2}`

`D = [ 5(3 + \sqrt{3})/2 + (1 + \sqrt{3}) - 3(\sqrt{3} + 2) ] . (5 + \sqrt{3})`

`D = [ (15 + 5\sqrt{3})/2 - 2\sqrt{3} - 5 ] . (5 + \sqrt{3})`

`D = [ (15 + 5\sqrt{3} - 4\sqrt{3} - 10)/2 ] . (5 + \sqrt{3})`

`D = [ (5 + \sqrt{3})/2 ] . (5 + \sqrt{3})`

`D = (5 + \sqrt{3})^2 / 2`

`D = (25 + 10\sqrt{3} + 3) / 2`

`D = (28 + 10\sqrt{3}) / 2`

`D = 14 + 5\sqrt{3}`