Kết quả của phép trừ $\frac{2}{{\left(x+1\right)}^2}-\frac{1}{x^2-1}$ là

A. $\frac{3-x}{\left(x-1\right){\left(x+1\right)}^2}$.

B. $\frac{x-3}{\left(x-1\right){\left(x+1\right)}^2}$.

C. $\frac{x-3}{{\left(x+1\right)}^2}$.

D. $\frac{1}{\left(x-1\right){\left(x+1\right)}^2}$.

Đáp án đúng là: B

Ta có: $\frac{2}{{\left(x+1\right)}^2}-\frac{1}{x^2-1}=\frac{2}{{\left(x+1\right)}^2}-\frac{1}{\left(x+1\right)\left(x-1\right)}$

         $=\frac{2\left(x-1\right)}{{\left(x+1\right)}^2\left(x-1\right)}-\frac{x+1}{{\left(x+1\right)}^2\left(x-1\right)}$

         $=\frac{2x-2-\left(x+1\right)}{{\left(x+1\right)}^2\left(x-1\right)}$

         $=\frac{2x-2-x-1}{{\left(x+1\right)}^2\left(x-1\right)}$

          $=\frac{x-3}{{\left(x+1\right)}^2\left(x-1\right)}$.