Question

化简分式

2/a-1除（2/a²-1加1/a+1） 请写下详细过程谢谢

Answer 1

如果是：2/a-1除（2/a²-1加1/a+1），则：
[2/(a²-1)+1/(a+1)]÷2/(a-1)
=[2/(a+1)(a-1)+(a-1)/(a+1)(a-1)]×(a-1)/2
=(a+1)/(a+1)(a-1)×(a-1)/2
=1/2
如果是：2/a-1除以（2/a²-1加1/a+1），则：
2/(a-1)÷[2/(a²-1)+1/(a+1)]
=2/(a-1)×[(a+1)(a-1)/(a+1)]
=2/(a-1)×(a-1)
=2

Answer 2

1、2/a²-1=2/(a+1)(a-1)
2、进行分母有理化：原式分母=（2+a-1）/a²-1=a+1/a²-1=a+1/(a+1)(a-1)=1/a-1
3、原式=2/a-1除以1/a-1=2