Question

計算：(

a+1

2a-2

-

3

2a2-2

-

a+3

2a+2

)×

4a2-4

3

．

Answer 1

分析：原式括號中三項通分并利用同分母分式的減法法則計算，約分即可得到結果．

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

．

點評：此題考查了分式的混合運算，分式的加減運算關鍵是通分，通分的關鍵是找最簡公分母；分式的乘除運算關鍵是約分，約分的關鍵是找公因式．