`A=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}`
`=\sqrt{\frac{(3\sqrt{3}-4)(2\sqrt{3}-1)}{(2\sqrt{3})^2-1^2}}-\sqrt{\frac{(\sqrt{3}+4)(5+2\sqrt{3})}{5^2-(2\sqrt{3})^2}}`
`=\sqrt{\frac{18-3\sqrt{3}-8\sqrt{3}+4}{12-1}-\sqrt{\frac{5\sqrt{3}+6+20+8\sqrt{3}}{25-12}}`
`=\sqrt{\frac{22-11\sqrt{3}}{11}}-\sqrt{\frac{26+13\sqrt{3}}{13}}`
`=\sqrt{\frac{11(2-\sqrt{3})}{11}}-\sqrt{\frac{13(2+\sqrt{3})}{13}}`
`=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}`
`=\frac{\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}][\sqrt{2}}`
`=\frac{\sqrt{(\sqrt{3}-1)^2}-\sqrt{(\sqrt{3}+1)^2}}{\sqrt{2}}`
`=\frac{|\sqrt{3}-1|-|\sqrt{3}+1|}{\sqrt{2}}=\frac{\sqrt{3}-1-\sqrt{3}-1}{\sqrt{2}}`
`=\frac{-2}{\sqrt{2}}=-\sqrt{2}`
`#tnvt`
