问题 解答题
化简分式:(x+
1
x
)2-[x+
1
x
-
1
1-x-
1
x
]2÷
x2+
1
x2
-x-
1
x
+3
x2+
1
x2
-2x-
2
x
+3
答案

x+1
x
=a,则x2+
1
x2
=(x+
1
x
)2-2
=a2-2.

原式=a2-(a-

1
1-a
2÷
a2-2-a+3
a2-2-2a+3

=a2-(

a2-a+1
a-1
)2÷
a2-a+1
(a-1)2

=a2-(a2-a+1)

=a-1

=x+

1
x
-1=
x2-x+1
x

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