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