问题 解答题
先化简,再求值:(
2x-3
x
-1)÷
x2-9
x
,其中x=97.
答案

方法一:

原式=

2x-3-x
x
÷
x2-9
x
(1分)

=

x-3
x
x
x2-9
(2分)

=

x-3
x
x
(x+3)(x-3)
(3分)

=

1
x+3
.(4分)

当x=97时,

1
x+3
=
1
100
.(5分)

方法二:

原式=

2x-3
x
÷
x2-9
x
-1÷
x2-9
x

=

2x-3
x
x
x2-9
-
x
x2-9
(2分)

=

2x-3
x
x
(x-3)(x+3)
-
x
(x-3)(x+3)
(3分)

=

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

=

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

=

1
x+3
.(4分)

当x=97时,

1
x+3
=
1
100
.(5分)

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