Trả lời bởi giáo viên
Đáp án đúng: b
Ta có \(\dfrac{{{x^2} + 4}}{{x - 2}} - \dfrac{{4x}}{{2 - x}} = \dfrac{{{x^2} + 4}}{{x - 2}} + \dfrac{{4x}}{{x - 2}} = \dfrac{{{x^2} + 4x + 4}}{{x - 2}}\)\( = \dfrac{{{{\left( {x + 2} \right)}^2}}}{{x - 2}}\) nên A sai.
* \(\dfrac{{{x^2} + 4}}{{x - 2}} + \dfrac{{4x}}{{2 - x}}\)\( = \dfrac{{{x^2} + 4}}{{x - 2}} - \dfrac{{4x}}{{x - 2}} = \dfrac{{{x^2} - 4x + 4}}{{x - 2}} = \dfrac{{{{\left( {x - 2} \right)}^2}}}{{x - 2}} = x - 2\) nên B đúng.
* \(\dfrac{{2x}}{{x - 2}} + \dfrac{4}{{{x^2} - 4}}\)\( = \dfrac{{2x}}{{x - 2}} + \dfrac{4}{{\left( {x - 2} \right)\left( {x + 2} \right)}} = \dfrac{{2x\left( {x + 2} \right) + 4}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} = \dfrac{{2{x^2} + 4x + 4}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\) nên C sai.
* \(\dfrac{{{x^2}}}{{x - 2}} - \dfrac{4}{{x - 2}}\)\( = \dfrac{{{x^2} - 4}}{{x - 2}} = \dfrac{{\left( {x - 2} \right)\left( {x + 2} \right)}}{{x - 2}} = x + 2\) nên D sai.
