问题 填空题
已知x=
3
-1
y=
3
+1
,则
x+
xy
xy
+y
+
xy
-y
x-
xy
的值是______.
答案

xy=(

3
-1)(
3
+1)=3-1=2,

则原式=

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

=

x2-y2
x
xy
+xy-xy-y
xy

=

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

=

x+y
xy

x=

3
-1,y=
3
+1
时,原式=
2
3
2
=
6

故答案是:

6

单项选择题
单项选择题