8. In the Cartesian plane, the graph of the function $y=\frac{2 x-1}{x-1}$ is reflected about the line $y=-x$. What is the equation for the graph of the image of the reflection?
(A) $y=\frac{x-1}{2 x+1}$
(B) $y=\frac{x-1}{x+2}$
(C) $y=\frac{2 x-1}{x+1}$
(D) $y=\frac{x+1}{x-2}$
(E) $y=\frac{-1-x}{2+x}$
8. Ans: E
We simply replace $x$ by $-y$ and $y$ by $-x$ to get
$$
\begin{aligned}
-x=\frac{2(-y)-1}{-y-1} & \Longrightarrow x y+x=-2 y-1 \\
& \Longrightarrow y=\frac{-1-x}{2+x}
\end{aligned}
$$