问题 解答题
计算.
(1)a+b+
2b2
a-b

(2)(x+1-
3
x-1
x+2
2x-2

(3)(2+
1
a-1
-
1
a+1
)÷(a-
a
1-a2
)
,其中a=2.
答案

(1)a+b+

2b2
a-b

=

(a+b)(a-b)
a-b
+
2b2
a-b

=

a2+b2
a-b

(2)(x+1-

3
x-1
x+2
2x-2

=[

(x+1)(x-1)
x-1
-
3
x-1
2(x-1)
x+2

=

(x+2)(x-2)
x-1
×
2(x-1)
x+2

=2x-4;

(3)(2+

1
a-1
-
1
a+1
)÷(a-
a
1-a2
),

=[

2(a+1)(a-1)
(a+1)(a-1)
+
(a+1)
(a-1)(a+1)
-
a-1
(a+1)(a-1)
]÷[
a(a+1)(a-1)
(a+1)(a-1)
+
a
(a+1)(a-1)
]

=

2a2
(a+1)(a-1)
×
(a+1)(a-1)
a3

=

2
a

把a=2代入原式得:原式=

2
a
=1.

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