Question

已知：x=

2

-1，求(

x-1

x2+x

-

x

x2+2x+1

)÷

1

x

的值．

Answer 1

原式=[

x-1

x(x+1)

-

x

(x+1) 2

]•x
=

(x-1)(x+1)-x2

x(x+1) 2

•x
=

x2-1-x2

(x+1)2

=-

1

(x+1) 2

，
当x=

2

-1时，原式=-

1

( 2 -1+1)2

=-

1

2

．