\(A=\dfrac{1-\sqrt{x-1}}{\sqrt{x-1-2\sqrt{x-1}+1}}=\dfrac{1-\sqrt{x-1}}{\sqrt{\left(\sqrt{x-1}-1\right)^2}}\)
\(A=\dfrac{1-\sqrt{x-1}}{\left|\sqrt{x-1}-1\right|}\) \(\Leftrightarrow\left[{}\begin{matrix}A=\dfrac{1-\sqrt{x-1}}{\sqrt{x-1}-1}=-1\\A=\dfrac{1-\sqrt{x-1}}{-\sqrt{x-1}+1}=1\end{matrix}\right.\)
\(B=\sqrt{8+2\sqrt{10+2\sqrt{5}}}-\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
\(B^2=\left(\sqrt{8+2\sqrt{10+2\sqrt{5}}}-\sqrt{8-2\sqrt{10+2\sqrt{5}}}\right)^2\)
\(B^2=8+2\sqrt{10+2\sqrt{5}}-2\sqrt{8+2\sqrt{10+2\sqrt{5}}}.\sqrt{8-2\sqrt{10+2\sqrt{5}}}+8-2\sqrt{10+2\sqrt{5}}\)
\(B^2=16-2\sqrt{\left(8+2\sqrt{10+2\sqrt{5}}\right)\left(8-2\sqrt{10+2\sqrt{5}}\right)}\)
\(B^2=16-2\sqrt{8^2-4\left(10+2\sqrt{5}\right)}\)
\(B^2=16-2\sqrt{24-8\sqrt{5}}\)
\(B^2=16-2\sqrt{\left(2\sqrt{5}-2\right)^2}\)
\(B^2=16-4\sqrt{5}+4=20-4\sqrt{5}\)
\(B=\sqrt{20-4\sqrt{5}}\)
