问题 解答题
课堂上,朱老师出了这样一道题:已知x=2009-5
3
,求代数式
x2-2x+1
x2-1
÷(1+
x-3
x+1
)
的值.小明觉得直接代入计算太繁了,请你来帮他解决,并写出具体过程.
答案

x2-2x+1
x2-1
÷(1+
x-3
x+1
)=
(x-1)2
(x+1)(x-1)
÷(
x+1
x+1
+
x-3
x+1

=

(x-1)2
(x+1)(x-1)
÷
2(x-1)
x+1

=

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

=

1
2

单项选择题
单项选择题