证：|(a²-1)/(a²+1)|=|(a²+1-2)/(a²+1)|=|1-2/(a²+1)|因为 a²>0，所以a²+1>1=> 0<2/(a²+1)<2=> -1<1-2/(a²+1)<1=> |(a²-1)/(a²+1)|<1
