计算化简：xx2+3x+2+xx2+x-2+21-x2．

题型：解答题难度：一般来源：不详

计算化简：

x

x2+3x+2

+

x

x2+x-2

+

2

1-x2

．

答案

原式=

x

(x+2)(x+1)

+

x

(x+2)(x-1)

+

2

(1+x)(1-x)

=

x(x-1)

(x+2)(x+1)(x-1)

+

x(x+1)

(x+2)(x+1)(x-1)

-

2(x+2)

(x+2)(x+1)(x-1)

=

x2-x +x2+x-2x-4

(x+2)(x2-1)

=

2x2-2x-4

(x+2)(x+1)(x-1)

=

2(x-2)(x+1)

(x+2)(x+1)(x-1)

=

2x-4

x2+x-2

．