Giải thích các bước giải:
a, ĐKXĐ: \(x \ne \pm 1\)
\(\begin{array}{l}
P = \frac{{2x}}{{{x^2} - 1}}:\left( {\frac{2}{{{x^2} - 1}} + \frac{1}{{x + 1}}} \right)\\
= \frac{{2x}}{{{x^2} - 1}}:\left( {\frac{2}{{{x^2} - 1}} + \frac{{x - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}} \right)\\
= \frac{{2x}}{{{x^2} - 1}}:\left( {\frac{{2 + x - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}} \right)\\
= \frac{{2x}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}.\frac{{\left( {x - 1} \right)\left( {x + 2} \right)}}{{x + 1}}\\
= \frac{{2x}}{{x + 1}}
\end{array}\)
b,
\(x = - 2\frac{1}{3} = \frac{{ - 7}}{3} \Rightarrow P = \frac{{ - \frac{7}{3}.2}}{{ - \frac{7}{3} + 1}} = \frac{7}{2}\)
c,
\(P = 0 \Leftrightarrow \frac{{2x}}{{x + 1}} = 0 \Leftrightarrow x = 0\)