x²-x-1=0x²=x+1x^4=(x+1)²=x²+2x+1=(x+1)+2x+1=3x+2x^5=x^4*x=(3x+2)*x=3x²+2x=3(x+1)+2x=5x+3(x^4+2x+1)/x^5=[(3x+2)+2x+1]/(5x+3)=(5x+3)/(5x+3)=1