6.29 Among the following four pairs of functions, the pair with the same graph shape is
(A) $y=\log _{3} x^{2}$ and $y=2 \log _{3} x$.
(B) $y=x^{2}$ and $y=10^{\lg x^{2}}$.
(C) $y=\frac{2}{x}$ and $y=\frac{x+1}{x-1}$.
(D) $y=\frac{x^{2}-x-2}{x^{2}-3 x+2}$ and $y=\frac{x+1}{x-1}$.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991)
[Solution] From $y=\frac{x+1}{x-1}=1+\frac{2}{x-1}$, its graph can be obtained by shifting the graph of $y=\frac{2}{x}$ one unit to the right and then one unit up, so their graphs have the same shape.
Therefore, the answer is $(C)$.

