解:lim(x->1)[(x²-1)/(x-1)]=lim(x->1)[(x+1)(x-1)/(x-1)] (分解因式) =lim(x->1)[x(x-1)/(x-1)] (分子分母同除(x-1)) =lim(x->1)x (分子分母同除(x-1)) =1