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

\(\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

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.

sai đề rồi bạn.\(\frac{a}{b}>\frac{a+c}{b+c}\) với \(a>b\) mới đúng nha.

Ta có:\(A=\frac{10^{17}+1}{10^{16}+1}>\frac{10^{17}+1+9}{10^{16}+1+9}=\frac{10^{17}+10}{10^{16}+10}=\frac{10\left(10^{16}+1\right)}{10\left(10^{15}+1\right)}=\frac{10^{16}+1}{10^{15}+1}\)

\(\Rightarrow A>B\)

:DDDDDD

giúp mình với mai phải nộp rồi

\(\frac{10^{15}+1}{10^{16}+1}=\frac{10^{16}+10}{10^{17}+10}\)

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

Vậy B<A

Ta có: \(10A=\frac{10^{16}+10}{10^{16}+1}=1+\frac{9}{10^{16}+1}\) ; \(10B=\frac{10^{17}+10}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

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

Ta có:

10A=10¹⁶+10/10¹⁶+1=1+​​(9/10¹⁶+1)

10B=10¹⁷+10/10¹⁷+1=1+(9/10¹⁷+1)

Vì 9/10¹⁶+1 > 9/10¹⁷+1 nên 10A>10B,do đó A>B