(1-x)^3=1-x^3-3x+3x^2,∴1-x^3=(1-x)^3+(3x-3x^2)=(1-x)^3+3x(1-x)=(1-x)[(1-x)^2+3x]=(1-x)(1+x+x^2),
lim x→1 [1/(1-x)]-[3/(1-x)^3]
=lim x→1 [(1+x+x^2)/(1-x)(1+x+x^2)]-[3/(1-x)(1+x+x^2)]
=lim x→1 (x^2+x-2)/(1-x)(1+x+x^2)
=lim x→1 -(1-x)(x+2)/(1-x)(1+x+x^2)
=lim x→1 -(x+2)/(1+x+x^2)
=-1.