x²-3x+1=0
x+1/x=3
﹙x+1/x﹚²=3²
x²+1/x²=7
∵﹙x^6+x³+1﹚/x³
=x³+1/x³+1
=﹙x+1/x﹚﹙x²-1+1/x²﹚+1
=3×﹙7-1﹚+1
=18+1
=19
∴ x³/﹙x^6+x³+1﹚=1/19.
x²-3x+1=0
x+1/x=3
﹙x+1/x﹚²=3²
x²+1/x²=7
∵﹙x^6+x³+1﹚/x³
=x³+1/x³+1
=﹙x+1/x﹚﹙x²-1+1/x²﹚+1
=3×﹙7-1﹚+1
=18+1
=19
∴ x³/﹙x^6+x³+1﹚=1/19.