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.

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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.

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.
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.

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.
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

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