Question

计算：(

a+1

2a-2

-

3

2a2-2

-

a+3

2a+2

)×

4a2-4

3

．

Answer 1

分析：原式括号中三项通分并利用同分母分式的减法法则计算，约分即可得到结果．

解答：解：原式=[

(a+1)2

2(a+1)(a-1)

-

3

2(a+1)(a-1)

-

(a+3)(a-1)

2(a+1)(a-1)

]•

4(a+1)(a-1)

3

=

1

2(a+1)(a-1)

•

4(a+1)(a-1)

3

=

2

3

．

点评：此题考查了分式的混合运算，分式的加减运算关键是通分，通分的关键是找最简公分母；分式的乘除运算关键是约分，约分的关键是找公因式．