limx→1((1/1-x)-(3/1-x^3))刚学

Question

limx→1((1/1-x )- (3/1-x^3))
刚学

Answer 1

limx→1((1/1-x )- (3/1-x^3))
=limx→1{(x^2+x+1)[/(1-x)(x^2+x+1)]-(3/1-x^3)}
=limx→1[(x^2+x+1-3)/(1-x^3)]
=limx→1[x^2+x-2)/(1-x^3)]
=limx→1[(x-1)(x+2)/(1-x)(1+x+x^2)]
=limx→1[-(x+2)/(1+x+x^2)]
=[-(1+2)/(1+1+1)]
=-1