2010008408
Level:
A
Solve the following equation with unknown \(x\) and a real parameter \(a\in\mathbb{R}\setminus\{1\}\).
\[\frac{x} {1-a} = a-x\]
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline
a=2 & \emptyset \\
a\notin\{1;2\} & \frac{a-a^2}{2-a}
\\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline
a=2 & \mathbb{R} \\
a\notin\{1;2\} & \frac{a-a^2}{2-a}
\\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline
a=2 & \mathbb{R} \\
a\notin\{1;2\} & \emptyset
\\\hline \end{array}\)