`A=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}`

`A=(\sqrt{2}(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}))/(\sqrt{2})`

`A=(\sqrt{2(2-\sqrt{3})}-\sqrt{2(2+\sqrt{3})})/(\sqrt{2})`

`A=(\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}})/(\sqrt{2})`

`A=(\sqrt{3-2\sqrt{3}+1}-\sqrt{3+2\sqrt{3}+1})/(\sqrt{2})`

`A=(\sqrt{(\sqrt{3}-1)^2}-\sqrt{(\sqrt{3}+1)^2})/(\sqrt{2})`

`A=(|\sqrt{3}-1|-|\sqrt{3}+1|)/(\sqrt{2})`

`A=(\sqrt{3}-1-\sqrt{3}-1)/(\sqrt{2})`

`A=(-2)/(\sqrt{2})`

`A=-\sqrt{2}`