Question

先化簡，再求值：（

3x+2

x2-1

）+

x

x+1

，其中x=（-1）²⁰¹²+tan60°．

Answer 1

原式=

3x+2

(x+1)(x-1)

+

x(x-1)

(x+1)(x-1)

=

3x+2+x2-x

(x+1)(x-1)

=

2x+2+x2

(x+1)(x-1)

=

(x+1)2+1

(x+1)(x-1)

，
∵x=（-1）²⁰¹²+tan60°=1+

3

，
∴原式=

(1+ 3 +1)2+1

(1+ 3 +1)(1+ 3 -1)

=

(2+ 3 )2+1

(2+ 3 )× 3

=

4+3+4 3 +1

2 3 +3

=

4(2+ 3 )

2 3 +3

=

4 3

3

．