若x＞1，则

x2-2x+2

2x-2

=

(x-1)2+1

2(x-1)

=

x-1

2

+

1

2(x-1)

≥2

x-1 2 • 1 2(x-1)

=1，当且仅当

x-1

2

=

1

2(x-1)

时，取等号．

故

x2-2x+2

2x-2

有最小值为1，

故选A．