\(10A=\frac{10^{16}+10}{10^{16}+1}=\frac{10^{16}+1+9}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)

\(10B=\frac{10^{17}+10}{10^{17}+1}=\frac{10^{17}+1+9}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

Nhận thấy: \(\frac{9}{10^{17}+1}< \frac{9}{10^{16}+1}\)=> 10B < 10A

=> A > B

A = ( 10^15+1 ) / ( 10^16+1 ) => 10A = ( 10^16+10 ) / ( 10^16+1 ) = 1 + ( 9/10^15+1 )

B = ( 10^16+1 ) / ( 10^17+1 ) => 10B = ( 10^17+10 ) / ( 10^17+1 ) = 1 + ( 9/10^16+1 )

Vì 10^15+1 < 10^16+1 nên 9/10^15+1 > 9/10^16+1 => 1 + ( 9/10^15+1 ) > 1 + ( 9/10^16+1 )

Vậy A > B

theo đè bài 

A>B

hok tốt

Ta có :

\(10A=\frac{10^{16}+10}{10^{16}+1}=\frac{\left(10^{16}+1\right)+9}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)

\(10B=\frac{10^{17}+10}{10^{17}+1}=\frac{\left(10^{17}+1\right)+9}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

Vì \(10^{16}+1< 10^{17}+1\) nên \(\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\) \(\Rightarrow1+\frac{9}{10^{16}+1}>1+\frac{9}{10^{17}+1}\)

=> 10A > 10B Do đó A > B

Vậy A > B

\(A=\frac{10^{15}+1}{10^{16}+1}\)

\(B=\frac{10^{16}+1}{10^{17}+1}\)

Ta có:

\(A=\frac{10^{15}+1}{10^{16}+1}=\frac{\left(10^{15}+1\right).10}{\left(10^{16}+1\right).10}=\frac{10^{16}+10}{10^{17}+10}=\frac{10^{16}+1+9}{10^{17}+1+9}\)

Vì \(B=\frac{10^{16}+1}{10^{17}+1}< 1\)

\(\Rightarrow B=\frac{10^{16}+1}{10^{17}+1}< \frac{10^{16}+1+9}{10^{17}+1+9}=A\)

Vậy B < A

A=1/10

B=1/10

Vậy hai phân số A và B bằng nhau

\(A=\frac{10^{15}+1}{10^{16}+1}\)

\(\Rightarrow10A=\frac{10^{16}+10}{10^{16}+1}=\frac{\left(10^{16}+1\right)+9}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)

\(A=\frac{10^{16}+1}{10^{17}+1}\)

\(\Rightarrow10B=\frac{10^{17}+10}{10^{17}+1}=\frac{\left(10^{17}+1\right)+9}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

Vì \(\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\left(Do10^{16}+1< 10^{17}+1\right)\)

\(\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

vì B<1 => \(B=\frac{10^{2013}+1}{10^{2014}+1}< \frac{10^{2013}+1+9}{10^{2014}+1+9}=\)\(\frac{10^{2013}+10}{10^{2014}+10}=\frac{10\left(10^{2012}+1\right)}{10\left(10^{2013}+1\right)}\)\(=\frac{10^{2012}+1}{10^{2013}+1}=A\)

\(\Rightarrow A>B\)

\(\frac{10^{2012}+1}{10^{2013}+1}=\frac{\left(10^{2012}+1\right)\cdot10}{\left(10^{2013}+1\right)\cdot10}=\frac{10^{2013}+10}{\left(10^{2013}+1\right)\cdot10}=\frac{10^{2013}+1+9}{\left(10^{2013}+1\right)\cdot10}=\frac{10^{2013}+1}{\left(10^{2013}+1\right)\cdot10}+\frac{9}{\left(10^{2013}+1\right)\cdot10}=\frac{1}{10}+\frac{9}{\left(10^{2013}+1\right)\cdot10}\left(1\right)\)

\(\frac{10^{2013}+1}{10^{2014}+1}=\frac{\left(10^{2013}+1\right)\cdot10}{\left(10^{2014}+1\right)\cdot10}=\frac{10^{2014}+10}{\left(10^{2014}+1\right)\cdot10}=\frac{10^{2014}+1+9}{\left(10^{2014}+1\right)\cdot10}=\frac{10^{2014}+1}{\left(10^{2014}+1\right)\cdot10}+\frac{9}{\left(10^{2014}+1\right)\cdot10}=\frac{1}{10}+\frac{9}{\left(10^{2014}+1\right)\cdot10}\left(2\right)\)Từ (1)(2) => A > B

giúp mình với mai phải nộp rồi

nhân cả tử và mẫu của a cho 10 ta được A=10^2008/10^2009 (nhân cả tử và mẫu cho 1 số thì giá trị của A vẫn k đổi em nhé)

so sánh A=10^2008/10^2009 với B=10^2008/10^2009 vì cùng tử và 2 mẫu bằng nhau nên A=B

Ta có:

\(A=\frac{10^{15}+1}{10^{16}+1}\)

\(10A=\frac{10^{16}+10}{10^{16}+1}\)

\(B=\frac{10^{16}+1}{10^{17}+1}\)

\(10B=\frac{10^{17}+10}{10^{17}+1}\)

Ta so sánh \(10A\) và \(10B\)

Có: 

\(10A:\) Mẫu - tử = 9

\(10B:\) Mẫu - tử = 9

Lại có:

 \(\frac{10^{16}+10}{10^{16}+1}\) \(-1\)\(=\frac{9}{10^{16}+1}\)

\(\frac{10^{17}+10}{10^{17}+1}-1=\frac{9}{10^{17}+1}\)

Vì \(\frac{9}{10^{16}+1}\)\(>\frac{9}{10^{17}+1}\)nên \(10A>10B\)

\(\Rightarrow\)\(A>B\)

Vậy \(A>B\)

Theo bải ra ta có:

A=\(\frac{10^{15}+1}{10^{16}+1}\)=> 10A =.\(\frac{10.\left(10^{15}+1\right)}{10^{16}+1}\)= \(\frac{10.10^{15}+1.10}{10^{16}+1}\)

                                      = \(\frac{10.10^{15}+10}{10^{16}+1}\)=\(\frac{10^{16}+1+9}{10^{16}+1}\)= \(1+\frac{9}{10^{16}+1}\)

B= \(\frac{10^{16}+1}{10^{17}+1}\)=> 10B = \(\frac{10.\left(10^{16}+1\right)}{10^{17}+1}\)=\(\frac{10.10^{16}+1.10}{10^{17}+1}\)

                                       = \(\frac{10.10^{16}+10}{10^{17}+1}\)= \(\frac{10^{17}+1+9}{10^{17}+1}\)= \(1+\frac{9}{10^{17}+1}\)

Vì 1=1 mà \(\frac{9}{10^{16}+1}\)>   \(\frac{9}{10^{17}+1}\)nên => 10A > 10B => A>B

Vậy A>B.