by Rút gọn: \(P = \left( {\frac{{\sqrt x + 1}}{{\sqrt x – 1}} + \frac{{\sqrt x }}{{2 + \sqrt x }} – \frac{{4x + 2\sqrt x – 4}}{{x – 4}}} \right)\left( {\frac{2}{{2 – \sqrt x }} – \frac{{\sqrt x + 3}}{{2\sqrt x – x}}} \right)\)
A \(P=\frac{4(x-2\sqrt{x}+2)(\sqrt{x}-3)}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}-2)}\)
B \(P=\frac{2(x-2\sqrt{x}+2)(\sqrt{x}-3)}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}+2)}\)
C \(P=\frac{2(x-2\sqrt{x}+2)(\sqrt{x}-3)}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}-2)}\)
D \(P=\frac{2(x-2\sqrt{x}+2)(\sqrt{x}-7)}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}-2)}\)
Hướng dẫn Chọn đáp án là: C
Phương pháp giải:
Quy đồng và rút gọn biểu thức.
Lời giải chi tiết:
\(\begin{array}{l}P = \left( {\frac{{\sqrt x + 1}}{{\sqrt x – 1}} + \frac{{\sqrt x }}{{2 + \sqrt x }} – \frac{{4x + 2\sqrt x – 4}}{{x – 4}}} \right)\left( {\frac{2}{{2 – \sqrt x }} – \frac{{\sqrt x + 3}}{{2\sqrt x – x}}} \right)\\P = \frac{{\left( {\sqrt x + 1} \right)\left( {x – 4} \right) + \sqrt x \left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right) – \left( {4x + 2\sqrt x – 4} \right)\left( {\sqrt x – 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}.\frac{{2\sqrt x – \left( {\sqrt x + 3} \right)}}{{\sqrt x \left( {2 – \sqrt x } \right)}}\\P = \frac{{\left( {x\sqrt x + x – 4\sqrt x – 4} \right) + \left( {x\sqrt x – 3x + 2\sqrt x } \right) – \left( {4x\sqrt x – 2x – 6\sqrt x + 4} \right)}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}.\frac{{\sqrt x – 3}}{{\sqrt x \left( {2 – \sqrt x } \right)}}\\P = \frac{{ – 2x\sqrt x + 4\sqrt x – 8}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}.\frac{{\sqrt x – 3}}{{\sqrt x \left( {2 – \sqrt x } \right)}}\\P = \frac{{ – 2.\left( {x\sqrt x + 8 – 2\sqrt x – 4} \right)}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}.\frac{{\sqrt x – 3}}{{\sqrt x \left( {2 – \sqrt x } \right)}}\\P = \frac{{ – 2.\left[ {\left( {\sqrt x + 2} \right)\left( {x – 2\sqrt x + 4} \right) – 2\left( {\sqrt x + 2} \right)} \right]}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}.\frac{{\sqrt x – 3}}{{\sqrt x \left( {2 – \sqrt x } \right)}}\\P = \frac{{2\left( {\sqrt x + 2} \right)\left( {x – 2\sqrt x + 2} \right)\left( {\sqrt x – 3} \right)}}{{\sqrt x \left( {\sqrt x – 1} \right){{\left( {\sqrt x – 2} \right)}^2}\left( {\sqrt x + 2} \right)}}\\P = \frac{{2\left( {x – 2\sqrt x + 2} \right)\left( {\sqrt x – 3} \right)}}{{\sqrt x \left( {\sqrt x – 1} \right){{\left( {\sqrt x – 2} \right)}^2}}}\end{array}\)
