Question

请你先化简分式

x+3

x2-1

÷

x2+6x+9

x2-2x+1

+

1

x+1

，再取恰当x的值代入求值．

Answer 1

x+3

x2-1

÷

x2+6x+9

x2-2x+1

+

1

x+1

=

x+3

(x+1)(x-1)

•

(x-1)2

(x+3)2

+

1

x+1

=

1

x+1

•

x-1

x+3

+

1

x+1

=

1

x+1

(

x-1

x+3

+1)
=

1

x+1

•

2(x+1)

x+3

=

2

x+3

，
∵x²-1≠0，x+3≠0，x-1≠0，x+1≠0，
∴取x=2，
代入得：原式=

2

2+3

=

2

5

．