Tháng Tư 16, 2024

Rút gọn biểu thức: \( N = \left( {{1 \over {\sqrt x – 3}} – {1 \over {\sqrt x }}} \right):\left( {{{\sqrt x + 3} \over {\sqrt x – 2}} – {{\sqrt x + 2} \over {\sqrt x – 3}}} \right)\) với \( x > 0;\,\,x \ne 4;\,\,x \ne 9.\) A \( N= \frac{-6-3\sqrt{x}}{5\sqrt{x}}\) B \( N= \frac{6+3\sqrt{x}}{5\sqrt{x}}\) C \( N= \frac{-6+3\sqrt{x}}{5\sqrt{x}}\) D \( N= \frac{6-3\sqrt{x}}{5\sqrt{x}}\)

Rút gọn biểu thức: \( N = \left( {{1 \over {\sqrt x – 3}} – {1 \over {\sqrt x }}} \right):\left( {{{\sqrt x + 3} \over {\sqrt x – 2}} – {{\sqrt x + 2} \over {\sqrt x – 3}}} \right)\) với \( x > 0;\,\,x \ne 4;\,\,x \ne 9.\)

A \( N= \frac{-6-3\sqrt{x}}{5\sqrt{x}}\)

B \( N= \frac{6+3\sqrt{x}}{5\sqrt{x}}\)

C \( N= \frac{-6+3\sqrt{x}}{5\sqrt{x}}\)

D \( N= \frac{6-3\sqrt{x}}{5\sqrt{x}}\)

Hướng dẫn Chọn đáp án là: D

Lời giải chi tiết:

\( \eqalign{ & N = \left( {{1 \over {\sqrt x – 3}} – {1 \over {\sqrt x }}} \right):\left( {{{\sqrt x + 3} \over {\sqrt x – 2}} – {{\sqrt x + 2} \over {\sqrt x – 3}}} \right) \cr & \,\,\,\,\, = {{\sqrt x – \sqrt x + 3} \over {\sqrt x \left( {\sqrt x – 3} \right)}}:{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right) – \left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)} \over {\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)}} \cr & \,\,\,\,\,\, = {3 \over {\sqrt x \left( {\sqrt x – 3} \right)}}:{{x – 9 – x + 4} \over {\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)}} \cr & \,\,\,\,\,\, = {3 \over {\sqrt x \left( {\sqrt x – 3} \right)}}.{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)} \over { – 5}}\, = {{ – 3\left( {\sqrt x – 2} \right)} \over {5\sqrt x }} = {{6 – 3\sqrt x } \over {5\sqrt x }}. \cr} \)

Chọn D.