问题 解答题
先化简,再求值:
x
y(x+y)
-
y
x(x+y)
,其中x=
2
+1,y=
2
-1
答案

原式=

x2
xy(x+y)
-
y2
xy(x+y)

=

x2-y2
xy(x+y)

=

(x-y)(x+y)
xy(x+y)

=

x-y
xy

x=

2
+1,y=
2
-1时,

x-y
xy
=
(
2
+1)-(
2
-1)
(
2
+1)(
2
-1)
=
2
1
=2

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