问题 填空题
x
x2+x+1
=a
,则
x2
x4+x2+1
=______.
答案

x2
x4+x2+1
=
x2
(x2+x+1)(x2-x+1)

=(

x
x2+x+1
)(
x
(x2+x+1)-2x
)

=

x
x2+x+1
1
x2+x+1
x
-2
,把
x
x2+x+1
=a
代入得:

1
1
a
-2
=
a2
1-2a

故答案为:

a2
1-2a

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