问题 解答题
已知M=
x2+y2
x2-y2
,N=
2xy
x2-y2
,用加减号连接M、N的三种不同形式:N+M.M-N,N-M,请你任选两种形式进行计算.
答案

∵M=

x2+y2
x2-y2
,N=
2xy
x2-y2

∴N+M=

x2+y2+2xy
x2-y2
=
(x+y)2
(x+y)(x-y)
=
x+y
x-y
;N-M=
x2+y2-2xy
x2-y2
=
(x-y)2
(x+y)(x-y)
=
x-y
x+y

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