\(A=\dfrac{\left(1-\sqrt{3}\right)^2-\left(1+\sqrt{3}\right)^2}{\left(1+\sqrt{3}\right)\left(1-\sqrt{3}\right)}:\sqrt{12}\)
\(A=\dfrac{\left(1-\sqrt{3}+1+\sqrt{3}\right)\left(1-\sqrt{3}-1-\sqrt{3}\right)}{1-3}:\sqrt{12}\)
\(A=\dfrac{2\left(-2\sqrt{3}\right)}{-2}:\sqrt{12}\)
\(A=2\sqrt{3}:\sqrt{12}=1\)