试题

题目：

化简

x2+1

x2-1

-

x-2

x-1

÷

x-2

2

，并用你喜欢的一个x的值求代数式的值．

答案

解：原式=

x2+1

(x+1)(x-1)

-

x-2

x-1

·

x

x-2

=

x2+1

(x+1)(x-1)

-

x

x-1

=

x2+1

(x+1)(x-1)

-

x(x+1)

(x+1)(x-1)

=

x2+1-x2-x

(x+1)(x-1)

=

1-x

(x+1)(x-1)

=-

1

x+1

；
当x=5时，原式=-

1

x+1

=-

1

5+1

=-

1

6

．
解：原式=

x2+1

(x+1)(x-1)

-

x-2

x-1

·

x

x-2

=

x2+1

(x+1)(x-1)

-

x

x-1

=

x2+1

(x+1)(x-1)

-

x(x+1)

(x+1)(x-1)

=

x2+1-x2-x

(x+1)(x-1)

=

1-x

(x+1)(x-1)

=-

1

x+1

；
当x=5时，原式=-

1

x+1

=-

1

5+1

=-

1

6

．

考点梳理

分式的化简求值．

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