Giải thích các bước giải:
ĐKXĐ: \(x \ne \pm 1\)
Ta có:
\(\begin{array}{l}
\frac{1}{{x + 1}} - \frac{1}{{x - 1}} - \frac{{2{x^2}}}{{1 - {x^2}}}\\
= \frac{1}{{x + 1}} - \frac{1}{{x - 1}} + \frac{{2{x^2}}}{{{x^2} - 1}}\\
= \frac{1}{{x + 1}} - \frac{1}{{x - 1}} + \frac{{2{x^2}}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{\left( {x - 1} \right) - \left( {x + 1} \right) + 2{x^2}}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{ - 2 + 2{x^2}}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{2{x^2} - 2}}{{{x^2} - 1}}\\
= 2
\end{array}\)
