如题.已知:X^-1+Y^-1=5,求分式(2X-XY+2Y)/(X+2XY+Y)的值.要有具体步骤.
问题描述：
如题.
已知:X^-1+Y^-1=5,求分式(2X-XY+2Y)/(X+2XY+Y)的值.
要有具体步骤.
答
X^-1+Y^-1=1/x+1/y=(x+y)/xy=5,所以x+y=5xy
(2X-XY+2Y)/(X+2XY+Y)
=（2（x+y）-xy）/(x+y+2xy)
=(2*5xy-xy)/(5xy+2xy)
=9xy/7xy
=9/7
答
分子分母同时除以xy得:
原式=(2/y -1 +2/x)/(1/y + 2 + 1/x)
=(10-1)/(5+2)
=9/7