问题 填空题
已知t=
4xy
x+y
,x≠0,y≠0,x≠y,则
t+2x
t-2x
+
t+2y
t-2y
=______.
答案

t=

4xy
x+y

t
2x
=
2y
x+y

t+2x
2x
=
x+3y
x+y
t-2x
2x
=
y-x
x+y

t+2x
t-2x
=
x+3y
y-x
.同理可得:
t+2y
t-2y
=
y+3x
x-y

∴原式=

x+3y
y-x
+
y+3x
x-y

=2.

故答案为:2

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