a, Để C có nghĩa <=> \(\left\{{}\begin{matrix}2x-2\ne0\\2-2x^2\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x\ne2\\2x^2\ne2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)\(\Leftrightarrow x\ne\pm1\) thì C có nghĩa.
b, \(\dfrac{x}{2x-2}+\dfrac{x^2+1}{2-2x^2}=\dfrac{x}{2\left(x-1\right)}+\dfrac{-\left(x^2+1\right)}{2\left(x^2-1\right)}\)
\(=\dfrac{x}{2\left(x-1\right)}+\dfrac{-\left(x^2+1\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}+\dfrac{-\left(x^2+1\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+x-x^2-1}{2\left(x-1\right)\left(x+1\right)}=\dfrac{x-1}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{2\left(x+1\right)}\)
c, \(C=-0,5\Leftrightarrow\dfrac{1}{2\left(x+1\right)}=-0,5\)
\(\Leftrightarrow2\left(x+1\right)=\dfrac{1}{-0,5}=-2\Leftrightarrow x+1=-1\Leftrightarrow x=-2\)
Vậy....