问题 解答题
(1)请从下 * * 个代数式中任选两个构造一个分式,并化简该分式.a2-1,ab-b,b+ab.
(2)先化简,再求值:(
a+2
a-2
+
4
a2-4a+4
a
a-2
,其中a=
1
2
答案

(1)

a2-1
ab-b
=
(a+1)(a-1)
b(a-1)
=
a+1
b

a2-1
b+ab
=
(a+1)(a-1)
b(1+a)
=
a-1
b

ab-b
a2-1
=
b(a-1)
(a+1)(a-1)
=
b
a+1

ab-b
b+ab
=
b(a-1)
(a+1)b
=
a-1
a+1

b+ab
a2-1
=
b(a+1)
(a+1)(a-1)
=
b
a-1

b+ab
ab-b
=
b(a+1)
b(a-1)
=
a+1
a-1

(2)原式=

a2-4+4
(a-2)2
÷
a
a-2

=

a2
(a-2)2
×
a-2
a

=

a
a-2

当a=

1
2
时,原式=
1
2
1
2
-2
=-
1
3

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