$$\eqalign{ & j)\,\,A = {{\sqrt {x - 2\sqrt {x - 1} } + \sqrt {x + 2\sqrt {x - 1} } } \over {\sqrt {{1 \over {{x^2}}} - {2 \over x} + 1} }}\,\,\left( {x > 1} \right) \cr & = {{\sqrt {x - 1 - 2\sqrt {x - 1} + 1} + \sqrt {x - 1 + 2\sqrt {x - 1} + 1} } \over {\sqrt {{{\left( {{1 \over x}} \right)}^2} - 2{1 \over x} + 1} }} \cr & = {{\sqrt {{{\left( {\sqrt {x - 1} - 1} \right)}^2}} + \sqrt {{{\left( {\sqrt {x - 1} + 1} \right)}^2}} } \over {\sqrt {{{\left( {{1 \over x} - 1} \right)}^2}} }} \cr & = {{\left| {\sqrt {x - 1} - 1} \right| + \sqrt {x - 1} + 1} \over {\left| {{1 \over x} - 1} \right|}} \cr & Do\,x > 1 \Rightarrow {1 \over x} < 1 \Rightarrow {1 \over x} - 1 < 0 \Rightarrow \left| {{1 \over x} - 1} \right| = 1 - {1 \over x} \cr & \Rightarrow A = {{\left| {\sqrt {x - 1} - 1} \right| + \sqrt {x - 1} + 1} \over {1 - {1 \over x}}} \cr & A = {{x\left[ {\left| {\sqrt {x - 1} - 1} \right| + \sqrt {x - 1} + 1} \right]} \over {x - 1}} \cr & Neu\,\,\sqrt {x - 1} - 1 < 0 \Leftrightarrow x - 1 < 1 \Leftrightarrow x < 2 \Rightarrow 1 < x < 2 \cr & \Rightarrow A = {{x\left[ {1 - \sqrt {x - 1} + \sqrt {x - 1} + 1} \right]} \over {x - 1}} = {{2x} \over {x - 1}} \cr & Neu\,\,\sqrt {x - 1} - 1 \ge 0 \Leftrightarrow x - 1 \ge 1 \Leftrightarrow x \ge 2 \cr & \Rightarrow A = {{x\left[ {\sqrt {x - 1} - 1 + \sqrt {x - 1} + 1} \right]} \over {x - 1}} = {{2x\sqrt {x - 1} } \over {x - 1}} = {{2x} \over {\sqrt {x - 1} }} \cr} $$