f(x)=a/(x-1)+1/(x+a)为奇函数,则
f(-x)=-f(x)
a/(-x-1)+1/(-x+a)=-a/(x-1)-1/(x+a)
a[1/(x-1)-1/(x+1)]=1/(x-a)-1/(x+a)
2a/(x^2-1)=2a/(x^2-a)
2a[1/(x^2-1)-1/(x^2-a)]=0
a=0或1/(x^2-1)=1/(x^2-a)
实数a=0或a=1