Question

化简：(1+

1

x-2

)÷

x2-2x+1

x2-4

．

Answer 1

分析：首先计算括号内的式子，然后对第二个分式的分子分母分解因式，转化成乘法运算，最后进行约分解求解．

解答：解：原式=

x-1

x-2

÷

x2-2x+1

x2-4

=

x-1

x-2

÷

(x-1)2

(x+2)(x-2)

=

x-1

x-2

•

(x+2)(x-2)

(x-1)2

=

x+2

x-1

．

点评：本题主要考查分式的混合运算，通分、因式分解和约分是解答的关键．