(2010•攀枝花三模)不等式x−1x>0成立的充分不必要条件是(  ) A.x>1 B.x<-1或0<x<1 C.x>-1 D.-1<x<0或x>1

问题描述:

(2010•攀枝花三模)不等式x−

1
x
>0成立的充分不必要条件是(  )
A. x>1
B. x<-1或0<x<1
C. x>-1
D. -1<x<0或x>1

不等式x−

1
x
>0,解得x>1或x<0
x>1⇒x>1或x<0,符合题意,故正确;
x<-1或0<x<1⇒x>1或x<0是假命题,故不正确;
x>-1⇒x>1或x<0是假命题,故不正确;
-1<x<0或x>1⇒x>1或x<0是假命题,故不正确;
故选:A