Question

计算：(

x+1

x-1

+

1

x2-2x+1

)÷

x2

x-1

Answer 1

分析：括号里的最简公分母为（x-1）²，化简后把除法统一为乘法，化简即可．

解答：解：原式=[

(x+1)(x-1)

(x-1)2

+

1

(x-1)2

]•

x-1

x2

=

x2

(x-1)2

•

x-1

x2

=

1

x-1

．
故答案为

1

x-1

．

点评：本题主要考查分式的混合运算，解答本题关键是通分和约分，注意把除法运算转化成乘法运算．