`#tnvt`
`\frac{\sqrt{20}-5}{2-\sqrt{5}}+\frac{12}{1+\sqrt{5}}`
`=\frac{\sqrt{5}(2-\sqrt{5})}{2-\sqrt{5}}+\frac{12(1-\sqrt{5})}{(1-\sqrt{5})(1+\sqrt{5})}`
`=\sqrt{5}+\frac{12(1-\sqrt{5})}{1-5}`
`=\sqrt{5}-3(1-\sqrt{5})`
`=\sqrt{5}-3+3\sqrt{5}`
`=4\sqrt{5}-3`
`\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\frac{1}{2-\sqrt{3}}`
`=\frac{\sqrt{3}(\sqrt{5}-2)}{\sqrt{5}-2}-\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}`
`=\sqrt{3}-\frac{2+\sqrt{3}}{4-3}`
`=\sqrt{3}-2-\sqrt{3}`
`=-2`
`\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}`
`=\sqrt{9-2.3.\sqrt{6}+6}+\sqrt{24-2.3.2\sqrt{6}+9}`
`=\sqrt{(3-\sqrt{6})^2}+\sqrt{(2\sqrt{6}-3)^2}`
`=|3-\sqrt{6}|+|2\sqrt{6}-3|`
`=3-\sqrt{6}+2\sqrt{6}-3`
`=\sqrt{6}`
`\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}`
`=\sqrt{45-2.3\sqrt{5}.1+1}-\sqrt{20-2.2\sqrt{5}.3+9}`
`=\sqrt{(3\sqrt{5}-1)^2}-\sqrt{(2\sqrt{5}-3)^2}`
`=|3\sqrt{5}-1|-|2\sqrt{5}-3|`
`=3\sqrt{5}-1-2\sqrt{5}+3`
`=\sqrt{5}+2`
