问题 解答题
先化简再求值:
(1)
2x
x-3
+
x
3-x
,其中x=-1;        
(2)(
3a
a-1
-
a
a+1
)•
a2-1
a
,其中a=2.
(3)(1+
1
a2-1
a
a-1
,其中a=-3.   
(4)(
1
a-2
+
1
a+2
2a
a2-4a+4
,其中a=-4.
答案

(1)原式=

2x-x
x-3
=
x
x-3
,当x=-1时,原式=
-1
-1-3
=
1
4

(2)原式=(

3a
a-1
-
a
a+1
)•
(a+1)(a-1)
a
=
3a
a-1
(a+1)(a-1)
a
-
a
a+1
(a+1)(a-1)
a
=3(a+1)-(a-1)=2a+4,当a=2时,原式=4+4=8;

(3)原式=[1+

1
(a+1)(a-1)
]•
a-1
a
=
a-1
a
+
1
a(a+1)
=
(a-1)(a+1)+1
a(a+1)
=
a2
a(a+1)
=
a
a+1
,当a=-3时,原式=
-3
-2
=
3
2

(4)原式=(

1
a-2
+
1
a+2
)•
(a-2)2
2a
=
1
a-2
(a-2)2
2a
+
1
a+2
(a-2)2
2a
=
a-2
2a
+
(a-2)2
2a(a+2)
=
(a-2)(a+2)+(a-2)2
2a(a+2)
=
2a2-4a
2a(a+2)
=
a-2
a+2
,当a=-4时,原式=
-6
-2
=3.

单项选择题