Question

[_Vũ_Bích_Diệp]

Soanhsgias trị phân số 

M=\(\frac{11^5+1}{11^6+1}\)với  N=\(\frac{11^6+1}{11^7+1}\)

Các bn giải từng bước ra cho mk nhé!

Ai nhanh mk tk cho

Answer 1

[Nguyễn Thanh Bình]

\(11M=\frac{11^6+11}{11^6+1}=\frac{11^6+1+10}{11^6+1}=\frac{11^6+1}{11^6+1}+\frac{10}{11^6+1}=1+\frac{10}{11^6+1}\)

\(11N=\frac{11^7+11}{11^7+1}=\frac{11^7+1+10}{11^7+1}=\frac{11^7+1}{11^7+1}+\frac{10}{11^7+1}=1+\frac{10}{11^7+1}\)

vì \(\frac{10}{11^6+1}>\frac{10}{11^7+1}\)

nên\(11M>11N\)

=>\(M>N\)

Answer 2

[Number one princess in the world]

\(M=\frac{11^5+1}{11^6+1}\)

\(\Rightarrow11M=11.\frac{11^5+1}{11^6+1}=\frac{11^6+11}{11^6+1}=\frac{11^6+1+10}{11^6+1}=1+\frac{10}{11^6+1}\)

\(N=\frac{11^6+1}{11^7+1}\)

\(\Rightarrow11N=11.\frac{11^6+1}{11^7+1}=\frac{11^7+11}{11^7+1}=\frac{11^7+1+10}{11^7+1}=1+\frac{10}{11^7+1}\)

Do \(1+\frac{10}{11^6+1}>1+\frac{10}{11^7+1}\)

\(\Rightarrow11M>11N\)

\(\Rightarrow M>N\)