Đáp án:
$\begin{array}{l}
\frac{x}{{2\left( {x - 1} \right)}} + \frac{{x - 2}}{{{x^2} - 1}} - \frac{5}{{2x + 2}}\left( {dkxd:x \ne \pm 1} \right)\\
= \frac{x}{{2\left( {x - 1} \right)}} + \frac{{x - 2}}{{\left( {x - 1} \right)\left( {x + 1} \right)}} - \frac{5}{{2\left( {x + 1} \right)}}\\
= \frac{{x\left( {x + 1} \right) + 2\left( {x - 2} \right) - 5\left( {x - 1} \right)}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{{x^2} + x + 2x - 4 - 5x + 5}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{{x^2} - 2x + 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{{{\left( {x - 1} \right)}^2}}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{x - 1}}{{2\left( {x + 1} \right)}}
\end{array}$
