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