Trả lời
Đáp án mình đưa ra hơi dài nha bạn:
[TEX]\frac{x^50+x^40+x^30+x^20+x^10+1}{x^45+x^40+x^35+x^30+x^25+x^20+x^15+x^10+1}[/TEX]
= [TEX]\frac{ x^10[x^10(x^30+x^20+x^10+1)+1]+1}{x^10[x^5(x^30+x^25+x^20+x^15+x^10+x^5+1)+1]+1}[/TEX]
= [TEX]\frac{x^10 . x^10(x^30+x^20+x^10+1)+2}{x^10 . x^5(x^30+x^25+x^20+x^15+x^10+x^5+1)+2}[/TEX]
= [TEX]\frac{x^20[x^10(x^20+x^10+1)+2 }{x^15[x^5(x^25+x^20+x^15+x^10+x^5+1)+1]+2}[/TEX]
= [TEX]\frac{x^20 . x^10(x^20+x^10+1)+3}{ x^15 . x^5(x^25+x^20+x^15+x^10+x^5+1)+3}[/TEX]
= [TEX]\frac{x^30[x^10(x^10+1)+1]+3}{x^20[x^5(x^20+x^15+x^10+x^5+1)+1]+3}[/TEX]
= [TEX]\frac{x^30 . x^10(x^10+1)+4}{ x^20 . x^5(x^20+x^15+x^10+x^5+1)+4}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^25(x^20+x^15+x^10+x^5+1)+4}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^25[x^5(x^15+x^10+x^5+1)+1]+4}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^25 . x^5(x^15+x^10+x^5+1)+5}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^30[x^5(x^10+x^5+1)+1]+5}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^30 . x^5(x^10+ x^5+1)+6}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^35[x^5(x^5+1)+1]+6}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^35 . x^5(x^5+1)+7}[/TEX]
= [TEX]\frac{x^40(x^10+1)+4}{x^40(x^5+1)+7}[/TEX]