当1\X－1\Y=2001,求分式(X-XY-Y)\(X-Y)的值!...x-y-xy/(x-y)=1-xy/(x-y）是杂得来的
问题描述：
当1\X－1\Y=2001,求分式(X-XY-Y)\(X-Y)的值!...
x-y-xy/(x-y)=1-xy/(x-y）是杂得来的
答
由1/x-1/y=2001得：y-x/xy=2001
所以：xy/y-x=1/2001 xy/x-y=-1/2001
x-xy-y/(x-y)=x-y-xy/(x-y)=1-xy/(x-y)
原式=1+1/2001=2002/2001
答
1/x-1/y=2001
(y-x)/xy=2001
y-x=2001xy
x-y=-2001xy
(x-xy-y)/(x-y)
=[(x-y)-xy]/(x-y)
=(-2001xy-xy)/(-2001xy)
=(-2002xy)/(-2001xy)
=2002/2001