by Rút gọn biểu thức: \(D = \left( {{{\sqrt x + \sqrt y } \over {1 – \sqrt {xy} }} – {{\sqrt x – \sqrt y } \over {1 + \sqrt {xy} }}} \right):\left( {{{y + xy} \over {1 – xy}}} \right)\) với \( x \ge 0;\,\,y \ge 0;\,\,xy \ne 1 \).
A \( D=-\frac{2}{\sqrt{y}}\)
B \( D=\frac{\sqrt{y}}{2}\)
C \( D=\frac{2}{\sqrt{y}}\)
D \( D=-\frac{\sqrt{y}}{2}\)
Hướng dẫn Chọn đáp án là: C
Lời giải chi tiết:
\( \eqalign{ & D = \left( {{{\sqrt x + \sqrt y } \over {1 – \sqrt {xy} }} – {{\sqrt x – \sqrt y } \over {1 + \sqrt {xy} }}} \right):\left( {{{y + xy} \over {1 – xy}}} \right) \cr & \,\,\,\,\, = {{\left( {\sqrt x + \sqrt y } \right)\left( {1 + \sqrt {xy} } \right) – \left( {\sqrt x – \sqrt y } \right)\left( {1 – \sqrt {xy} } \right)} \over {\left( {1 – \sqrt {xy} } \right)\left( {1 + \sqrt {xy} } \right)}}.{{1 – xy} \over {y + xy}} \cr & \,\,\,\,\, = {{\sqrt x + \sqrt y + x\sqrt y + y\sqrt x – \left( {\sqrt x – \sqrt y – x\sqrt y + y\sqrt x } \right)} \over {1 – xy}}.{{1 – xy} \over {y + xy}} \cr & \,\,\,\,\, = {{\sqrt x + \sqrt y + x\sqrt y + y\sqrt x – \sqrt x + \sqrt y + x\sqrt y – y\sqrt x } \over {y + xy}} \cr & \,\,\,\,\, = {{2\sqrt y + 2x\sqrt y } \over {y + xy}} = {{2\sqrt y \left( {x + 1} \right)} \over {y\left( {x + 1} \right)}} = {2 \over {\sqrt y }}. \cr} \)
Chọn C.
