Question

課堂上，朱老師出了這樣一道題：已知x=2009-5

3

，求代數式

x2-2x+1

x2-1

÷(1+

x-3

x+1

)的值．小明覺得直接代入計算太繁了，請你來幫他解決，并寫出具體過程．

Answer 1

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

．