化简求值:(2x/(x^2-y^2))-(1/(x-y)),其中x=(3根号5)-1,y=(-2根号5)+1

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化简求值:(2x/(x^2-y^2))-(1/(x-y)),其中x=(3根号5)-1,y=(-2根号5)+1

化简求值:(2x/(x^2-y^2))-(1/(x-y)),其中x=(3根号5)-1,y=(-2根号5)+1
化简求值:(2x/(x^2-y^2))-(1/(x-y)),其中x=(3根号5)-1,y=(-2根号5)+1

化简求值:(2x/(x^2-y^2))-(1/(x-y)),其中x=(3根号5)-1,y=(-2根号5)+1
(2x/(x²-y²))-(1/(x-y))
=2x/(x+y)(x-y)-(x+y)/(x+y)(x-y)
=(2x-x-y)/(x+y)(x-y)
=(x-y)/(x+y)(x-y)
=1/(x+y)
=1/(3√5-1-2√5+1)
=1/√5
=√5/5
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2x/(X+Y)(X-Y)-1/(X-Y)
=2x/(X+Y)(X-Y)-(x+y)/(x+y)(x-y)
=2x-x-y/(x+y)(x-y)
=x-y/(x+y)(x-y)
=1/(x+y)
因为X=3根号5-1 Y=-2根号5+1
所以原式=1/3根号5 -1-2根号5+1=1/根号5=根号5/5

(2x/(x^2-y^2))-(1/(x-y))
=(2x/(x^2-y^2))-(（x+y)/(x-y)（x+y))
=(2x/(x^2-y^2))-(（x+y)/(x^2-y^2))
=(2x-(x+y)/(x^2-y^2))
=(2x-x-y)/(x^2-y^2))
=(x-y)/(x^2-y^2))
=1/(x+y)
=1/[(3根号5)-1+(-2根号5)+1]
=1/[(3根号5)+(-2根号5)]
=1/根号5
=根号5/5

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