试题

题目：

计算：
（1）(

x2

x+2

-

4

x+2

)÷

x-2

x

（2）

x-1

x+2

÷

x2-2x+1

x2-4

+

1

x-1

．

答案

（1）解：原式=

x2-4

x+2

·

x

x-2

=

(x+2)(x-2)

x+2

·

x

x-2

=x；
（2）解：原式=

x-1

x+2

·

(x+2)(x-2)

(x-1)2

+

1

x-1

=

x-2

x-1

+

1

x-1

=

x-2+1

x-1

=1．

（2）原式=

x-1

x+2

·

x2-4

x2-2x+1

+

1

x-1

=

x-1

x+2

·

(x+2)(x-2)

(x-1)2

+

1

x-1

=

x-2

x-1

+

1

x-1

=

x-2+1

x-1

=

x-1

x-1

=1．
（1）解：原式=

x2-4

x+2

·

x

x-2

=

(x+2)(x-2)

x+2

·

x

x-2

=x；
（2）解：原式=

x-1

x+2

·

(x+2)(x-2)

(x-1)2

+

1

x-1

=

x-2

x-1

+

1

x-1

=

x-2+1

x-1

=1．

（2）原式=

x-1

x+2

·

x2-4

x2-2x+1

+

1

x-1

=

x-1

x+2

·

(x+2)(x-2)

(x-1)2

+

1

x-1

=

x-2

x-1

+

1

x-1

=

x-2+1

x-1

=

x-1

x-1

=1．

考点梳理

分式的混合运算．

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