lim【x→1】[1/(1-x)-3/(1-x³)]
=lim【x→1】[(1+x+x²)/(1-x³)-3/(1-x³)]
=lim【x→1】(x²+x-2)/(1-x³)
=lim【x→1】(x+2)(x-1)/[(1-x)(1+x+x²)]
=lim【x→1】-(x+2)/(1+x+x²)
=-(1+2)/(1+1+1²)
=-1