请教一道GWD数学

weiwei_zhwq

The operation Ä is defined for all nonzero numbers a and b by a Ä b = a/b – b/a.  If x and y are nonzero numbers, which of the following statements must be true?

I.                    x Ä xy = x(1 Ä y)

I.                    x Ä xy = x(1 Ä y)

II.                 x Ä y = -(y Ä x)

III.               1/x Ä 1/y = y Ä x

A.   I only

B.    II only

C.   III only

D.   I and II

E.    II and III

答案是E

可我怎么算出来I也是对的呢? 望NN们指教~

[此贴子已经被作者于2009-6-5 11:49:22编辑过]

h5641

 x Ä xy = 2/ xy - xy/x= 1/y -y

 x(1 Ä y) = x(1/x - y/1) = 1- xy

weiwei_zhwq

懂了, 非常感谢!!