Question

计算：（x^-1-y^-1）÷（x^-2-y^-2）-xy（x+y）^-1．

Answer 1

原式=（

1

x

-

1

y

）÷（

1

x2

-

1

y2

）-

xy

x+y

=

y-x

xy

÷

(y-x)(y+x)

x2y2

-

xy

x+y

=

y-x

xy

×

x2y2

(y-x)(y+x)

-

xy

x+y

=

xy

y+x

-

xy

x+y

=0．