`A=\sqrt{3}-\sqrt{2}-\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}`
`= \sqrt{3}-\sqrt{2}-(\sqrt{15}-\sqrt{12})(\sqrt{5}+2)`
`= \sqrt{3}-\sqrt{2}-(\sqrt{15}-2\sqrt{3})(\sqrt{5}+2)`
`= \sqrt{3}-\sqrt{2}-(\sqrt{75}+2\sqrt{15}-2\sqrt{15}-4\sqrt{3})`
`= \sqrt{3}-\sqrt{2}-(5\sqrt{3}-4\sqrt{3})`
`= -\sqrt{2}`
`B= \frac{\sqrt{7}+5}{-9}-\frac{\sqrt{7}-5}{-9}`
`= -\frac{\sqrt{7}+5}{9}+\frac{\sqrt{7}-5}{9}`
`= \frac{-(\sqrt{7}+5)+\sqrt{7}-5}{9}`
`= \frac{-\sqrt{7}-5+\sqrt{7}-5}{9}`
`= -10/9`
`C= \frac{(\sqrt{7}+\sqrt{5})(\sqrt{7}+\sqrt{5})}{2}+\frac{(\sqrt{7}-\sqrt{5})(\sqrt{7}-\sqrt{5})}{2}`
`= \frac{12+2\sqrt{35}}{2}+\frac{12-2\sqrt{35}}{2}`
`= 6+\sqrt{35}+6-\sqrt{35}`
`= 12`
`D= \sqrt{2}-1+\sqrt{3}-\sqrt{2}+\frac{1}{\sqrt{3}+2}`
`= -1+sqrt3-(sqrt3-2)`
`-1+sqrt3-sqrt3+2`
`= 1`
`E= \frac{sqrt3+sqrt2+1}{(sqrt3+sqrt2+1)(sqrt3+sqrt2-1)}`
`= \frac{sqrt3+sqrt2+1}{(sqrt3+sqrt2)^2-1}`
`= \frac{sqrt3+sqrt2+1}{4+2sqrt6}`
`= \frac{(sqrt3+sqrt2+1)(4-2sqrt6)}{(4+2sqrt6)(4-2sqrt6)}`
`= \frac{4sqrt3-2sqrt{18}+4sqrt2-2sqrt{12}-4+2sqrt6}{16-24}`
`= \frac{-2sqrt2-4-2sqrt6}{-8}`
`= -\frac{-sqrt2-1+sqrt6}{4}`
`F= \frac{sqrt5-sqrt3-2}{(sqrt5-sqrt3+2)(sqrt5-sqrt3-2)}`
`= \frac{sqrt5-sqrt3-2}{4-2sqrt{15}}`
`= \frac{(sqrt5-sqrt3-2)(4+sqrt{15})}{(4-sqrt{15})(4+sqrt{15})}`
`= \frac{4sqrt5+2sqrt{75}-4sqrt3-2sqrt{45}-8-4sqrt{15}}{16-60}`
`= \frac{-2sqrt5+6sqrt3-8-2sqrt{15}}{-44}`
`= -\frac{-sqrt5+3sqrt3-4-2sqrt{15}}{22}`
