问题 解答题
已知
x
y
=
1
3
,求
3x
x+y
-
x2-y2
x-y
3y
x2+2xy+y2
的值.
答案

3x
x+y
-
x2-y2
x-y
3y
x2+2xy+y2

=

3x
x+y
-
(x+y)(x-y)
x-y
3y
(x+y)2

=

3x
x+y
-
3y
x+y

=

3x-3y
x+y
.  

x
y
=
1
3
时,y=3x.

∴原式=

3x-9x
x+3x
=-
3
2

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