Đề bài

Kết quả của phép trừ \(\dfrac{2}{{{{(x + 1)}^2}}} - \dfrac{1}{{{x^2} - 1}}\) là: A. \(\dfrac{{3 - x}}{{(x - 1){{(x + 1)}^2}}}\) B. \(\dfrac{{x - 3}}{{(x - 1){{(x + 1)}^2}}}\) C. \(\dfrac{{x - 3}}{{{{(x + 1)}^2}}}\) D. \(\dfrac{1}{{(x - 1){{(x + 1)}^2}}}\)   

Lời giải chi tiết

Ta có:\(\dfrac{2}{{{{(x + 1)}^2}}} - \dfrac{1}{{{x^2} - 1}}\)\( = \dfrac{2}{{{{\left( {x + 1} \right)}^2}}} - \dfrac{1}{{\left( {x + 1} \right)\left( {x - 1} \right)}} = \dfrac{{2\left( {x - 1} \right)}}{{{{\left( {x + 1} \right)}^2}\left( {x - 1} \right)}} - \dfrac{{\left( {x + 1} \right)}}{{{{\left( {x + 1} \right)}^2}\left( {x - 1} \right)}}\)\( = \dfrac{{2x - 2 - x - 1}}{{{{\left( {x + 1} \right)}^2}\left( {x - 1} \right)}} = \dfrac{{x - 3}}{{{{\left( {x + 1} \right)}^2}\left( {x - 1} \right)}}\)Đáp án B