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`B={2}/{sqrt{5}-sqrt{2}}+{4}/{sqrt{6}+sqrt{2}}+{1}/{sqrt{6}+sqrt{5}}`

`={2(sqrt{5}+sqrt{2})}/{(sqrt{5}-sqrt{2})(sqrt{5}+sqrt{2})}+{4(sqrt{6}-sqrt{2})}/{(sqrt{6}-sqrt{2})(sqrt{6}+sqrt{2})}+{sqrt{6}-sqrt{5}}/{(sqrt{6}-sqrt{5})(sqrt{6}+sqrt{5})}`

`={2sqrt{5}+2sqrt{2}}/{(sqrt{5})^2-(sqrt{2})^2}+{4sqrt{6}-4sqrt{2}}/{(sqrt{6})^2-(sqrt{2})^2}+{sqrt{6}-sqrt{5}}/{(sqrt{6})^2-(sqrt{5})^2}`

`={2sqrt{5}+2sqrt{2}}/{3}+{4sqrt{6}-4sqrt{2}}/{4}+{sqrt{6}-sqrt{5}}/{1}`

`={4(2sqrt{5}+2sqrt{2})+3(4sqrt{6}-4sqrt{2})+12(sqrt{6}-sqrt{5})}/{12}`

`={8sqrt{5}+8sqrt{2}+12sqrt{6}-12sqrt{2}+12sqrt{6}-12sqrt{5}}/{12}`

`={24sqrt{6}-4sqrt{5}-4sqrt{2}}/{12}`

`={4(6sqrt{6}-sqrt{5}-sqrt{2})}/{12}={6sqrt{6}-sqrt{5}-sqrt{2}}/3`