已知2/x+2/y=根号24,求 x/y(x-y) - y/x(x-y)的值

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已知2/x+2/y=根号24,求 x/y(x-y) - y/x(x-y)的值
已知2/x+2/y=根号24,求 x/y(x-y) - y/x(x-y)的值

已知2/x+2/y=根号24,求 x/y(x-y) - y/x(x-y)的值
2/x+2/y=根号24
(2y+2x)/xy=2√6
x+y=xy√6
x/y(x-y) - y/x(x-y)
=1/(x-y)[(x/y-y/x)]
=1/(x-y)[(x²-y²)/xy]
=1/(x-y)[(x-y)(x+y)/xy]
=(x+y)/xy
=xy√6/xy
=√6

后面的式子通分，就变成了 (x+y)/xy
前面的式子通分是 2(x+y)/xy=根号24
所以后面的式子就是二分之根号24 化简就是根号6
这种题目只有一个条件对于后面那个式子就只能通分大胆计算试一试就出来了

x/[y(x-y)] - y/[x(x-y)]
=(x^-y^)/[xy(x-y)]
=(x+y)/(xy)
=1/x+1/y
=√6.

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