已知x =2y 化简（根号y/根号x -根号y )-(根号y/根号x +根号y)

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已知x =2y 化简（根号y/根号x -根号y )-(根号y/根号x +根号y)
已知x =2y 化简（根号y/根号x -根号y )-(根号y/根号x +根号y)

已知x =2y 化简（根号y/根号x -根号y )-(根号y/根号x +根号y)
（根号y/根号x -根号y )-(根号y/根号x +根号y)
=｛根号y（根号x+根号y）｝/（x-y）-｛根号y（根号x-根号y）｝/(x-y)
=(y+y)/(x-y)
因为x=2y
所以原式
=2y/y=2

原式=√y*[1/(√ x-√ y)-1/(√ x+√ y)
=√ y*[(√ x+√ y)/(x-y)-(√ x-√ y)/(x-y)]
=√ y*2√ y/(x-y)
=2y/(x-y)
=2y/(2y-y)
=2

原式=√y/(√2y-√y)-√y/(√2y+√y)
=√y/[√y(√2-1)]-√y/[√y(√2+1)]
=1/(√2-1)-1/(√2+1)
=(√2+1)/(√2+1)(√2-1)-(√2-1)/(√2+1)(√2-1)
=(√2+1)/(2-1)-(√2-1)/(2-1)
=√2+1-√2+1
=2

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