Q8:

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)

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

Answer: e

第一个左边=x/xy-xy/x=1/y-y 第一个右边=x(1/y-y) 所以第一个肯定错

第二个左边=x/y-y/x 第一个右边=-(y/x-x/y)=第二个左边 所以第二个对

第三个左边=(1/x/1/y-1/y/1/x)=y/x-x/y 第三个右边=y/x-x/y 所以第三个也对