limx趋于无穷大时求x[ln(x-2)-ln(x+1)]的极限

lim(x→∞) x[ln(x-2)-ln(x+1)]=lim(x->∞) [ln(x-2)-ln(x+1)]/(1/x)=lim(x→∞) [1/(x-2)-1/(x+1)]/(-1/x^2)=lim(x->∞) -[(x+1-x+2)/[(x-2)(x+1)]x^2=lim(x->∞) -3x^2/(x^2-x-2)=-3