问题 解答题
请你先化简分式
x+3
x2-1
÷
x2+6x+9
x2-2x+1
+
1
x+1
,再取恰当x的值代入求值.
答案

x+3
x2-1
÷
x2+6x+9
x2-2x+1
+
1
x+1

=

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

=

1
x+1
x-1
x+3
+
1
x+1

=

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

=

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

=

2
x+3

∵x2-1≠0,x+3≠0,x-1≠0,x+1≠0,

∴取x=2,

代入得:原式=

2
2+3
=
2
5

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