Rút gọn biểu thức A = 3/2x^2 + 2x + | 2x - 1|/x^2 - 1 - 2x biết x > 1/2, x khác 1. A. 1/2x( x - 1) B. 1/2x( x + 1) C. 2( x - 1)( x + 1) D. 2x( x - 1)( x + 1)

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Rút gọn biểu thức \[{\rm{A}} = \frac{3}{{2{{\rm{x}}^2} + 2{\rm{x}}}} + \frac{{\left| {2{\rm{x}} - 1} \right|}}{{{{\rm{x}}^2} - 1}} - \frac{2}{{\rm{x}}}\] biết\[{\rm{x}} > \frac{1}{2};\,\,\,{\rm{x}} \ne 1\].

\[\frac{1}{{2{\rm{x}}\left( {{\rm{x}} - 1} \right)}}\]

\[\frac{1}{{2{\rm{x}}\left( {{\rm{x}} + 1} \right)}}\]

\[\frac{2}{{\left( {{\rm{x}} - 1} \right)\left( {{\rm{x}} + 1} \right)}}\]

\[\frac{{2{\rm{x}}}}{{\left( {{\rm{x}} - 1} \right)\left( {{\rm{x}} + 1} \right)}}\]

Giải thích

Lời giải

Đáp án đúng là: A

\[{\rm{A}} = \frac{3}{{2{{\rm{x}}^2} + 2{\rm{x}}}} + \frac{{\left| {2{\rm{x}} - 1} \right|}}{{{{\rm{x}}^2} - 1}} - \frac{2}{{\rm{x}}}\]

\[ = \frac{3}{{2{{\rm{x}}^2} + 2{\rm{x}}}} + \frac{{2x - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}} - \frac{2}{{\rm{x}}}\]

\[ = \frac{{3\left( {x - 1} \right) + 2x\left( {2x - 1} \right) - 4\left( {x - 1} \right)\left( {x + 1} \right)}}{{2x\left( {x - 1} \right)\left( {x + 1} \right)}}\]

\[ = \frac{{3x - 3 + 4{x^2} - 2x - 4{x^2} + 4}}{{2x\left( {x - 1} \right)\left( {x + 1} \right)}}\]

\[ = \frac{{x + 1}}{{2x\left( {x - 1} \right)\left( {x + 1} \right)}} = \frac{1}{{2x\left( {x - 1} \right)}}\]