\[\begin{array}{l}
a)C = \frac{x}{{2{\rm{x}} - 2}} + \frac{{{x^2} + 1}}{{2 - 2{{\rm{x}}^2}}}\\
dk:\left\{ \begin{array}{l}
2{\rm{x}} - 2 \ne 0\\
2 - 2{{\rm{x}}^2} \ne 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ne 1\\
x \ne \pm 1
\end{array} \right.\\
\Leftrightarrow x \ne \pm 1\\
Vay:x \ne \pm 1\\
b)C = \frac{x}{{2{\rm{x}} - 2}} + \frac{{{x^2} + 1}}{{2 - 2{{\rm{x}}^2}}}\\
x \ne \pm 1\\
= \frac{x}{{2\left( {x - 1} \right)}} - \frac{{{x^2} + 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{x\left( {x + 1} \right) - {x^2} - 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{{x^2} + x - {x^2} - 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{{x - 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\
= \frac{1}{{2\left( {x + 1} \right)}}\\
Vay:C = \frac{1}{{2\left( {x + 1} \right)}}\left( {x \ne \pm 1} \right)\\
d)C > 0 = > \frac{1}{{2\left( {x + 1} \right)}} > 0\left( {x \ne \pm 1} \right)\\
= > 2\left( {x + 1} \right) > 0\\
= > x + 1 > 0\\
= > x > - 1\\
vay:x > - 1;x \ne 1thi:C > 0
\end{array}\]