求lim x2+2x+5/3x2-x+1怎么用那个公式求极限?

题目

求lim x2+2x+5/3x2-x+1怎么用那个公式求极限?
怎么一点点带进去?
x→∞

答案

原式=lim(x->∞)[(x²+2x+5)/(3x²-x+1)]
=lim(x->∞)[(1+2/x+5/x²)/(3-1/x+1/x²)]
=(1+2*0+5*0)/(3-0+0)
=1/3