Question

計算：(

x+1

x-1

+

1

x2-2x+1

)÷

x2

x-1

Answer 1

分析：括號里的最簡公分母為（x-1）²，化簡后把除法統一為乘法，化簡即可．

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

．
故答案為

1

x-1

．

點評：本題主要考查分式的混合運算，解答本題關鍵是通分和約分，注意把除法運算轉化成乘法運算．