Question

若x=

5

2

，则

x+1 - x-1

x+1 + x-1

+

x+1 + x-1

x+1 - x-1

．

Answer 1

考点：根式与分数指数幂的互化及其化简运算

专题：计算题

分析：把要求值的式子分母有理化，通分后化简，代入x的值得答案．

解答： 解：∵x=

5

2

，
∴

x+1 - x-1

x+1 + x-1

+

x+1 + x-1

x+1 - x-1

=

( x+1 - x-1 )2

( x+1 + x-1 )( x+1 - x-1 )

+

( x+1 + x-1 )2

( x+1 - x-1 )( x+1 + x-1 )

=

x+1-2 x2-1 +x-1

x+1-x+1

+

x+1+2 x2-1 +x-1

x+1-x+1

=

2x-2 x2-1

2

+

2x+2 x2-1

2

=

4x-2 x2-1 +2 x2-1

2

=2x=2×

5

2

=

5

．

点评：本题考查根式与分数指数幂的互化及其化简运算，关键是进行分母有理化，是基础题．