\(A=\frac{x-1}{\sqrt{y}-1}.\sqrt{\frac{\left(y-2\sqrt{y}+1\right)^2}{\left(x^2-2x+1\right)^2}}\)
\(=\frac{x-1}{\sqrt{y}-1}.\frac{\sqrt{\left(y-2\sqrt{y}+1\right)^2}}{\sqrt{\left(x^2-2x+1\right)^2}}\)
\(=\frac{x-1}{\sqrt{y}-1}.\frac{|y-2\sqrt{y}+1|}{|(x^2-2x+1)|}\)
\(=\frac{x-1}{\sqrt{y}-1}.\frac{\left(\sqrt{y}-1\right)^2}{\left(x-1\right)^2}=\frac{\sqrt{y}-1}{x-1}\)
\(đkxđ\Leftrightarrow\hept{\begin{cases}y\ge0\\x-1\ne0\end{cases}\Rightarrow\hept{\begin{cases}y\ge0\\x\ne1\end{cases}}}\)
\(A=\frac{x-1}{\sqrt{y}-1}\sqrt{\frac{\left(y-2\sqrt{y}+1\right)^2}{\left(x^2-2x+1\right)^2}}\)
\(=\frac{x-1}{\sqrt{y}-1}\sqrt{\frac{\left(\sqrt{y}-1\right)^2}{\left(x-1\right)^2}}\)
\(=\frac{\left(x-1\right)|\sqrt{y}-1|}{\left(\sqrt{y}-1\right)\left(x-1\right)}=\frac{|\sqrt{y}-1|}{\left(\sqrt{y}-1\right)}\)
TH1 : \(y>1\Rightarrow\sqrt{y}>1\Rightarrow\sqrt{y}-1>0\)
\(\Rightarrow|\sqrt{y}-1|=\sqrt{y}-1\)
\(\Rightarrow A=\frac{\sqrt{y}-1}{\sqrt{y}-1}=1\)
Th2 : \(0< y< 1\Rightarrow\sqrt{y}< 1\Rightarrow\sqrt{y}-1< 0\)
\(\Rightarrow|\sqrt{y}-1|=-\left(\sqrt{y}-1\right)\)
\(\Rightarrow A=\frac{-\left(\sqrt{y}-1\right)}{\sqrt{y}-1}=-1\)
KL : Nếu \(0< y< 1\Rightarrow A=-1\)
Nếu \(y>1\Rightarrow A=1\)
