由lin(x²-6x+5)/(x²-5x+4)x→∞=lim(x-1)(x-5)/(x-1)(x-4)x→∞=lim(x-5)/(x-4)x→∞=lim(1-5/x)/(1-4/x) (当x→∞时,5/x和4/x→0)x→∞=1 (所以原式极限为1)解法二:lim(1-6/x+5/x²)/(1-5/x+4/x²)(分子,分母同时除以x²,这个方法无论能否约分,都好用)x→∞=1 (直接=1)