Question

计算：

x3-1

x3+2x2+2x+1

+

x3+1

x3-2x2+2x+1

-

2(x2+1)

x2-1

．

Answer 1

考点：分式的混合运算

专题：计算题

分析：原式各项变形约分后，通分并利用同分母分式的加减法则计算即可得到结果．

解答：解：原式=

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

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

+

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

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

-

2(x2+1)

(x+1)(x-1)

=

x-1

x+1

+

x+1

x-1

-

2(x2+1)

(x+1)(x-1)

=

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

(x+1)(x-1)

=0．

点评：此题考查了分式的混合运算，熟练掌握运算法则是解本题的关键．