已知X/Y=5/3,求X/(X+Y)+X/(X-Y)-Y*2/(X*2-Y*2)的值.

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已知X/Y=5/3,求X/(X+Y)+X/(X-Y)-Y*2/(X*2-Y*2)的值.

已知X/Y=5/3,求X/(X+Y)+X/(X-Y)-Y*2/(X*2-Y*2)的值.
已知X/Y=5/3,求X/(X+Y)+X/(X-Y)-Y*2/(X*2-Y*2)的值.

已知X/Y=5/3,求X/(X+Y)+X/(X-Y)-Y*2/(X*2-Y*2)的值.
X/Y=5/3,求
X/(X+Y)+X/(X-Y)-Y^2/(X^2-Y^2)
=1/[1+(X/Y)]+1/[1-(X/Y)]-1/[(X^2/Y^2)-1]
=1/[1+5/3]+1/[1-5/3]-1/[(5/3)^2-1]
=1/(8/3)-1/(2/3)-1/[25/9-1]
=3/8-3/2-1/(16/9)
=3/8-3/2-9/16
=(3*2-3*8-9)/16
=(6-24-9)/16
=-27/16

因为X/Y=5/3，
X/(X+Y)+X/(X-Y)-Y^2/(X^2-Y^2)
=1/[1+(X/Y)]+1/[1-(X/Y)]-1/[(X^2/Y^2)-1]
=1/[1+5/3]+1/[1-5/3]-1/[(5/3)^2-1]
=1/(8/3)-1/(2/3)-1/[25/9-1]
=3/8-3/2-1/(16/9)
=3/8-3/2-9/16
=(3*2-3*8-9)/16
=(6-24-9)/16
=-27/16

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