`8/(3 + \sqrt{5}) - (\sqrt{15} - \sqrt{20})/(2 - \sqrt{3}) + \sqrt{(2\sqrt{5} - 7)^2}`

`= (8(3-\sqrt{5}))/(9-5) - (\sqrt{5}(\sqrt{3} - 2))/(2 - \sqrt{3})  + |2\sqrt{5} - 7|`

`= (8(3-\sqrt{5}))/(4) +(\sqrt{5}(2- \sqrt{3} ))/(2 - \sqrt{3})  + 7 - 2\sqrt{5}`

`=2(3 - \sqrt{5}) + \sqrt{5} + 7- 2\sqrt{5}`

`= 6 - 2\sqrt{5} + \sqrt{5} -2\sqrt{5} + 7`

`= 13 -3\sqrt{5}`